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Compound Interest Calculator

See how your savings and investment account balances can grow with the magic of compound interest.

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Using this compound interest calculator

Try your calculations both with and without a monthly contribution — say, $5 to $200, depending on what you can afford.

This savings calculator includes an example rate of return. To see the annual percentage yield you can expect, compare rates on NerdWallet for thousands of savings accounts and certificates of deposit .

» Ready to begin? Start saving with some of our favorite savings accounts or IRA providers .

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Betterment Cash Reserve – Paid non-client promotion

5.50% *Current promotional rate; annual percentage yield (variable) is 5.50% as of 4/2/24, plus a .50% boost available as a special offer with qualifying deposit. Terms apply; if the base APY increases or decreases, you’ll get the .75% boost on the updated rate. Cash Reserve is only available to clients of Betterment LLC, which is not a bank; cash transfers to program banks conducted through clients’ brokerage accounts at Betterment Securities.

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What is compound interest?

For savers, the definition of compound interest is basic: It’s the interest you earn on both your original money and on the interest you keep accumulating. Compound interest allows your savings to grow faster over time.

In an account that pays compound interest, such as a standard savings account, the return gets added to the original principal at the end of every compounding period, typically daily or monthly. Each time interest is calculated and added to the account, it results in a larger balance. With the compound interest formula, the account earns more interest in the next compounding period.

For example, if you put $10,000 into a savings account with a 4% annual yield, compounded daily, you’d earn $408 in interest the first year, $425 the second year, an extra $442 the third year and so on. After 10 years of compounding, you would have earned a total of $4,918 in interest.

But remember, that’s just an example. For longer-term savings, there are better places than savings accounts to store your money, including Roth or traditional IRAs and CDs .

Compounding investment returns

When you invest in the stock market, you don’t earn a set interest rate but rather a return based on the change in the value of your investment. When the value of your investment goes up, you earn a return.

If you leave your money and the returns you earn are invested in the market, those returns compound over time in the same way that interest is compounded.

If you invested $10,000 in a mutual fund and the fund earned a 6% return for the year, it means you gained $600, and your investment would be worth $10,600. If you got an average 6% return the following year, it means your investment would be worth $11,236.

Over the years, that money can really add up: If you kept that money in a retirement account over 30 years and earned that average 6% return, for example, your $10,000 would grow to more than $57,000.

In reality, investment returns will vary year to year and even day to day. In the short term, riskier investments such as stocks or stock mutual funds may actually lose value. But over a long time horizon, history shows that a diversified growth portfolio can return an average of 6% annually. Investment returns are typically shown at an annual rate of return.

Compounding can help fulfill your long-term savings and investment goals, especially if you have time to let it work its magic over years or decades. You can earn far more than what you started with.

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Compounding with additional contributions

As impressive as compound interest might be, progress on savings goals also depends on making steady contributions.

Let’s go back to the savings account example above and use the daily compound interest calculator to see the impact of regular contributions. We started with $10,000 and ended up with $4,918 in interest after 10 years in an account with a 4% annual yield. But by depositing an additional $100 each month into your savings account, you’d end up with $29,648 after 10 years, when compounded daily. The interest would be $7,648 on total deposits of $22,000.

To calculate interest without a calculator, use the formula A=P(1+r/n)^nt, where:

A = ending amount P = original balance r = interest rate (as a decimal) n = number of times interest is compounded in a specific timeframe t = time frame

Use the formula A=P(1+r/n)^nt. For example, say you deposit $5,000 in a savings account that earns a 3% annual interest rate, and compounds monthly. You’d calculate A = $5,000(1 + 0.03/12)^(12 x 1), and your ending balance would be $5,152. So after a year, you’d have $5,152 in savings.

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Interest calculation for 5 years

Disclaimer: Whilst every effort has been made in building our calculator tools, we are not to be held liable for any damages or monetary losses arising out of or in connection with their use. Full disclaimer .

Using our interest calculator

With our compound interest calculator you can calculate the interest you might earn on your savings, investment or 401k over a period of years and months based upon a chosen number of compounds per year.

Simply enter your initial investment (principal amount), interest rate, compound frequency and the amount of time you're aiming to save or invest for. You can include regular deposits or withdrawals within your calculation to see how they impact the future value.

What is compound interest?

The concept of compound interest, or 'interest on interest', is that accumulated interest is added back onto your principal sum, with future interest calculations being made on both the original principal and the already-accrued interest.

When you combine the power of interest compounding with regular, consistent investing over a sustained period of time, you end up with a highly effective growth strategy for accelerating the long-term value of your savings or investments.

How important is compound interest? Just ask Warren Buffett, one of the world's most successful investors:

How is compound interest calculated?

Compound interest is calculated using the compound interest formula: A = P(1+r/n)^nt . For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of the number of time periods (years). This gives a combined figure for principal and compound interest.

Let's break the compound interest formula down into its individual parts:

• A = the future value of the investment
• P = the principal balance
• r = the annual interest rate (decimal)
• n = number of times interest is compounded per year
• t = the time in years
• ^ = ... to the power of ...

How to calculate monthly compound interest

Here's how to calculate monthly compound interest using our compound interest formula. Monthly compound interest means that our interest is compounded 12 times per year:

• Divide your annual interest rate (decimal) by 12 and then add one to it.
• Raise the resulting figure to the power of the number of years multiplied by 12.
• Multiply your step 2 result by your principal balance (P).
• Deduct the principal balance from your step 3 result if you want just the interest.

As a formula, it looks like this:

A = P(1 + r/12)^12t

In our article about the compound interest formula , we go through the process of how to use the formula step-by-step, and give some real-world examples of how to use it.

For the remainder of the article, we'll look at how compound interest provides positive benefits for savings and investments.

See also: Simple Interest Calculator | Loan Calculator With Extra Payments

The benefits of compound interest

I think pictures really help with understanding concepts, and this situation is no different. The power of compound interest becomes obvious when you look at a graph of long-term growth.

Below is an example graph of an initial $1,000 investment. We'll use a longer investment compounding period (20 years) at 10% per year, to keep the sum simple.

As we compare the compound interest line in our graph to those for standard interest and no interest at all, it's clear to see how compound interest boosts the investment value over time.

What will $10,000 be worth in 20 years?

Let's break down the interest compounding by year with a more realistic example scenario. We'll say you have $10,000 in a savings account earning 5% interest per year, with annual compounding. We'll assume you intend to leave the investment untouched for 20 years. Your investment projection looks like this...

$10,000 invested at a fixed 5% yearly interest rate, compounded yearly, will grow to $26,532.98 after 20 years. This means total interest of $16,532.98 and a return on investment of 165%.

These example calculations assume a fixed percentage yearly interest rate. If you are investing your money, rather than saving it in fixed rate accounts, the reality is that returns on investments will vary year on year due to fluctuations caused by economic factors.

It is for this reason that the risk management strategy of diversification is widely recommended by industry experts.

Compounding with additional deposits

Combining interest compounding with regular deposits into your savings account, SIP , Roth IRA or 401(k) is a highly efficient saving strategy that can really boost the growth of your money in the longer term. 4

Looking back at our example from above, if we were to contribute an additional $100 per month into our investment, our balance after 20 years would hit the heights of $67,121, with interest of $33,121 on total deposits of $34,000.

As financial institutions point out, if people begin making regular investment contributions early on in their lives, they can see significant growth in their savings further down the road as their interest snowball gets larger and they gain benefit from Dollar-cost or Pound-cost averaging. 5

Where to invest for compound interest

The question about where to invest to earn the most compound interest has become a feature of our email inbox, with people thinking about mutual funds, ETFs, MMRs and high-yield savings accounts and wanting to know what's best.

We at The Calculator Site work to develop quality tools to assist you with your financial calculations. We can't, however, advise you about where to invest your money to achieve the best returns for you. Instead, we advise you to speak to a qualified financial advisor for advice based upon your own circumstances.

There are also some excellent articles from renowned financial websites that list ways to invest for compound interest. Here are two of the best articles, to help with your research:

• 12 Best Compound Interest Investments . Young and the Invested (author: Riley Adams).
• How to Use Compounding Interest Accounts . Motley Fool (author: Mike Price).

Let's cover some frequently asked questions about our compound interest calculator.

When is my interest compounded?

With savings and investments , interest can be compounded at either the start or the end of the compounding period. If additional deposits or withdrawals are included in your calculation, our calculator gives you the option to include them at either the start or end of each period.

Can I include regular withdrawals?

You can include regular withdrawals within your compound interest calculation as either a monetary withdrawal or as a percentage of interest/earnings. This can be used in combination with regular deposits.

You may, for example, want to include regular deposits whilst also withdrawing a percentage for taxation reporting purposes. Or, you may be considering retirement and wondering how long your money might last with regular withdrawals.

What is the effective annual interest rate?

The effective annual rate (also known as the annual percentage yield ) is the rate of interest that you actually receive on your savings or investment after compounding has been factored in.

When interest compounding takes place, the effective annual rate becomes higher than the nominal annual interest rate. The more times the interest is compounded within the year, the higher the effective annual interest rate will be.

What is RoR/TWR?

Within our compound interest calculator results section, you will see either a RoR or TWR figure appear for your calculation. You may be wondering what these are, so let's take a look.

The Rate of Return (RoR) is the percentage return on your investment over the entire investment term. We calculate it by taking the Initial investment figure away from the Final value, dividing the resulting figure by the Initial investment and then multiplying it by 100. The formula looks like this: 6

If you include regular deposits or withdrawals in your calculation, we switch to provide you with a Time-Weighted Return (TWR) figure .

The TWR figure represents the cumulative growth rate of your investment. It is calculated by breaking out each period's growth individually to remove the effects of any additional deposits and withdrawals. The TWR gives you a clearer picture of how your investment might have performed if you hadn't made extra deposits or withdrawn funds, allowing you to better assess its overall performance. You can learn more about TWR in this article by The Balance .

If you want to head back up to the calculator results area, you can click the link here . If you have any feedback or questions about the RoR or TWR, please contact us .

Before you go...

Here's a final thought . If you want to roughly calculate compound interest on a savings figure, without using a calculator, you can use a formula called the rule of 72 . The rule of 72 helps you estimate the number of years it will take to double your money. The method is simple - just divide the number 72 by your annual interest rate.

For example, let's say you're earning 3% per annum. Divide 72 by 3, which will give you 24. So, in about 24 years, your initial investment will have doubled. If you're receiving 6% then your money will double in about 12 years. All using the power of compound interest.

I hope you found this calculator and article useful. Many of the features in my compound interest calculator have come as a result of user feedback, so if you have any comments or suggestions, I would love to hear from you .

• Edward Hubbard, Percival Matthews & Anya Samek (2016). Using online compound interest tools to improve financial literacy , The Journal of Economic Education.
• Lusardi and Tufano (2015); Lusardi and de Bassa Scheresberg (2013); Stango and Zinman (2009); Behrman et al., (2012); Lusardi and Mitchell (2014). Financial Literacy Around the World .
• The emergence of compound interest , British Actuarial Journal, 2019.
• How a small savings account can get big over time . Federal Deposit Insurance Corporation.
• Saving earlier can help give you the power of compound interest on your savings . Canada Life.
• Rate of return . CFI Education Inc.

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Compound Interest Calculator

How to use the compound interest calculator, interest rate definition, what is the compound interest definition, simple vs. compound interest, compounding frequency, compound interest formula, compound interest examples, example 1 – basic calculation of the value of an investment, example 2 – complex calculation of the value of an investment, example 3 – calculating the interest rate of an investment using the compound interest formula, example 4 – calculating the doubling time of an investment using the compound interest formula, compound interest table, additional information, behind the scenes of compound interest calculator.

This compound interest calculator is a tool to help you estimate how much money you will earn on your deposit . In order to make smart financial decisions, you need to be able to foresee the final result. That's why it's worth knowing how to calculate compound interest. The most common real-life application of the compound interest formula is a regular savings calculation.

Read on to find answers to the following questions:

• What is the interest rate definition?
• What is the compound interest definition, and what is the compound interest formula?
• What is the difference between simple and compound interest rates?
• How to calculate compound interest?
• What are the most common compounding frequencies?

Our compound interest calculator is a versatile tool that helps you forecast the growth of your investments over time. To effectively use it, follow these instructions:

Enter initial balance : Start by inputting the amount you have initially invested or saved.

Input interest rate : Type in the annual interest rate your investment will earn.

Set the term : Determine the number of years and months over which you want the investment to grow.

Select Compounding Frequency : Choose how often the interest will be compounded. Options range from annually to daily.

Additional deposits : Decide if you'll make additional deposits. If so, specify the amount, how often, whether these are at the beginning or end of the compounding period, and their annual growth rate.

Review results : The calculator will display the final balance, total compound interest, and the breakdown of interest earned on the initial balance and additional deposits. It will also show the total principal amount and the sum of additional deposits made over the term.

Visualization : You can choose to represent your balance growth visually by selecting a bar graph, pie chart, table, or a combined chart and table view.

For example, with an initial balance of $1,000 and an 8% interest rate compounded monthly over 20 years without additional deposits, the calculator shows a final balance of $4,926.80. The total compound interest earned is $3,926.80.

Whether for personal savings, retirement planning, or educational investments, this calculator offers the foresight needed to make informed financial decisions.

Read on to learn more about the magic of compound interest and how it's calculated.

In finance, the interest rate is defined as the amount charged by a lender to a borrower for the use of an asset . So, for the borrower, the interest rate is the cost of the debt, while for the lender, it is the rate of return.

Note that in the case where you make a deposit into a bank (e.g., put money in your savings account), you have, from a financial perspective, lent money to the bank. In such a case, the interest rate reflects your profit.

The interest rate is commonly expressed as a percentage of the principal amount (outstanding loan or value of deposit). Usually, it is presented on an annual basis, which is known as the annual percentage yield (APY) or effective annual rate (EAR).

Generally, compound interest is defined as interest that is earned not solely on the initial amount invested but also on any further interest . In other words, compound interest is the interest on both the initial principal and the interest that has been accumulated on this principal so far. Therefore, the fundamental characteristic of compound interest is that interest itself earns interest . This concept of adding a carrying charge makes a deposit or loan grow at a faster rate.

You can use the compound interest equation to find the value of an investment after a specified period or estimate the rate you have earned when buying and selling some investments. It also allows you to answer some other questions, such as how long it will take to double your investment.

We will answer these questions in the examples below.

You should know that simple interest is something different than the compound interest . It is calculated only on the initial sum of money. On the other hand, compound interest is the interest on the initial principal plus the interest which has been accumulated.

Most financial advisors will tell you that compound frequency is the number of compounding periods in a year. But if you are not sure what compounding is, this definition will be meaningless to you… To understand this term, you should know that compounding frequency is an answer to the question How often is the interest added to the principal each year? In other words, compounding frequency is the time period after which the interest will be calculated on top of the initial amount .

For example:

• Annual (1/Yr) compounding has a compounding frequency of one ,
• Quarterly (4/Yr) compounding has a compounding frequency of four ,
• Monthly (12/Yr) compounding has a compounding frequency of twelve .

Note that the greater the compounding frequency is, the greater the final balance. However, even when the frequency is unusually high, the final value can't rise above a particular limit.

As the main focus of the calculator is the compounding mechanism, we designed a chart where you can follow the progress of the annual interest balances visually. If you choose a higher than yearly compounding frequency, the diagram will display the resulting extra or additional part of interest gained over yearly compounding by the higher frequency . Thus, in this way, you can easily observe the real power of compounding.

The compound interest formula is an equation that lets you estimate how much you will earn with your savings account. It's quite complex because it takes into consideration not only the annual interest rate and the number of years but also the number of times the interest is compounded per year.

The formula for annual compound interest is as follows:

• F V \mathrm{FV} FV – Future value of the investment, in our calculator it is the final balance
• P P P – Initial balance (the value of the investment);
• r r r – Annual interest rate (in decimal);
• m m m – Number of times the interest is compounded per year ( compounding frequency ); and
• t t t – Numbers of years the money is invested for.

It is worth knowing that when the compounding period is one ( m = 1 m = 1 m = 1 ), then the interest rate ( r r r ) is called the CAGR (compound annual growth rate): you can learn about this quantity at our CAGR calculator .

• Do you want to understand the compound interest equation?
• Are you curious about the fine details of how to calculate the compound interest rate?
• Are you wondering how our calculator works?
• Do you need to know how to interpret the results of compound interest calculation?
• Are you interested in all possible uses of the compound interest formula?

The following examples are there to try and help you answer these questions. We believe that after studying them, you won't have any trouble with understanding and practical implementation of compound interest.

The first example is the simplest, in which we calculate the future value of an initial investment.

You invest $10,000 for 10 years at the annual interest rate of 5%. The interest rate is compounded yearly. What will be the value of your investment after 10 years?

Firstly let’s determine what values are given and what we need to find. We know that you are going to invest $ 10000 \$10000 $10000 – this is your initial balance P P P , and the number of years you are going to invest money is 10 10 10 . Moreover, the interest rate r r r is equal to 5 % 5\% 5% , and the interest is compounded on a yearly basis, so the m m m in the compound interest formula is equal to 1 1 1 .

We want to calculate the amount of money you will receive from this investment. That is, we want to find the future value F V \mathrm{FV} FV of your investment.

To count it, we need to plug in the appropriate numbers into the compound interest formula:

The value of your investment after 10 years will be $16,288.95.

Your profit will be F V − P \mathrm{FV} - P FV − P . It is $ 16288.95 − $ 10000.00 = $ 6288.95 \$16288.95 - \$10000.00 = \$6288.95 $16288.95 − $10000.00 = $6288.95 .

Note that when doing calculations, you must be very careful with your rounding. You shouldn't do too much until the very end. Otherwise, your answer may be incorrect. The accuracy is dependent on the values you are computing. For standard calculations, six digits after the decimal point should be enough.

In the second example, we calculate the future value of an initial investment in which interest is compounded monthly.

You invest $10,000 at the annual interest rate of 5%. The interest rate is compounded monthly. What will be the value of your investment after 10 years?

Like in the first example, we should determine the values first. The initial balance P P P is $ 10000 \$10000 $10000 , the number of years you are going to invest money is 10 10 10 , the interest rate r r r is equal to 5 % 5\% 5% , and the compounding frequency m m m is 12 12 12 . We need to obtain the future value F V \mathrm{FV} FV of the investment.

Let's plug in the appropriate numbers in the compound interest formula:

The value of your investment after 10 years will be $ 16470.09 \$16470.09 $16470.09 .

Your profit will be F V − P \mathrm{FV} - P FV − P . It is $ 16470.09 − $ 10000.00 = $ 6470.09 \$16470.09 - \$10000.00 = \$6470.09 $16470.09 − $10000.00 = $6470.09 .

Did you notice that this example is quite similar to the first one? Actually, the only difference is the compounding frequency. Note that only thanks to more frequent compounding this time you will earn $ 181.14 \$181.14 $181.14 more during the same period: $ 6470.09 − $ 6288.95 = $ 181.14 \$6470.09 - \$6288.95 = \$181.14 $6470.09 − $6288.95 = $181.14 .

Now, let's try a different type of question that can be answered using the compound interest formula. This time, some basic algebra transformations will be required. In this example, we will consider a situation in which we know the initial balance, final balance, number of years, and compounding frequency, but we are asked to calculate the interest rate. This type of calculation may be applied in a situation where you want to determine the rate earned when buying and selling an asset (e.g., property) that you are using as an investment.

Data and question You bought an original painting for $2,000. Six years later, you sold this painting for $3,000. Assuming that the painting is viewed as an investment, what annual rate did you earn?

Solution Firstly, let's determine the given values. The initial balance P P P is $ 2000 \$2000 $2000 and final balance F V \mathrm{FV} FV is $ 3000 \$3000 $3000 . The time horizon of the investment is 6 6 6 years, and the frequency of the computing is 1 1 1 . This time, we need to compute the interest rate r r r .

Let's try to plug these numbers into the basic compound interest formula:

We can solve this equation using the following steps: Divide both sides by 2000 2000 2000 :

Raise both sides to the 1/6 th power:

Subtract 1 1 1 from both sides:

Finally solve for r r r :

In this example you earned $1,000 out of the initial investment of $2,000 within the six years, meaning that your annual rate was equal to 6.9913%.

As you can see this time, the formula is not very simple and requires a lot of calculations. That's why it's worth testing our compound interest calculator, which solves the same equations in an instant, saving you time and effort.

Have you ever wondered how many years it will take for your investment to double its value? Besides its other capabilities, our calculator can help you to answer this question. To understand how it does it, let's take a look at the following example.

Data and question

You put $1,000 in your savings account. Assuming that the interest rate is equal to 4% and it is compounded yearly, find the number of years after which the initial balance will double.

The given values are as follows: the initial balance P P P is $ 1000 \$1000 $1000 and final balance F V \mathrm{FV} FV is 2 ⋅ $ 1000 = $ 2000 2 \cdot \$1000 = \$2000 2 ⋅ $1000 = $2000 , and the interest rate r r r is 4 % 4\% 4% . The frequency of the computing is 1 1 1 . The time horizon of the investment t t t is unknown.

Let's start with the basic compound interest equation:

Knowing that m = 1 m = 1 m = 1 , r = 4 % r = 4\% r = 4% , and F V = 2 ⋅ P \mathrm{FV} = 2 \cdot P FV = 2 ⋅ P we can write:

Which could be written as:

Divide both sides by P P P ( P P P mustn't be 0 0 0 !):

To solve for t t t , you need take the natural log ( ln ⁡ \ln ln ), of both sides:

In our example, it takes 18 years (18 is the nearest integer that is higher than 17.67) to double the initial investment.

Have you noticed that in the above solution, we didn't even need to know the initial and final balances of the investment? It is thanks to the simplification we made in the third step ( Divide both sides by P P P ). However, when using our compound interest rate calculator, you will need to provide this information in the appropriate fields. Don't worry if you just want to find the time in which the given interest rate would double your investment; just type in any numbers (for example, 1 1 1 and 2 2 2 ).

It is also worth knowing that exactly the same calculations may be used to compute when the investment would triple (or multiply by any number, in fact). All you need to do is just use a different multiple of P in the second step of the above example. You can also do it with our calculator.

Compound interest tables were used every day before the era of calculators, personal computers, spreadsheets, and unbelievable solutions provided by Omni Calculator 😂. The tables were designed to make the financial calculations simpler and faster (yes, really…). They are included in many older financial textbooks as an appendix.

Below, you can see what a compound interest table looks like.

Using the data provided in the compound interest table, you can calculate the final balance of your investment. All you need to know is that the column compound amount factor shows the value of the factor ( 1 + r ) t (1 + r)^t ( 1 + r ) t for the respective interest rate (first row) and t (first column). So to calculate the final balance of the investment, you need to multiply the initial balance by the appropriate value from the table.

Note that the values from the column Present worth factor are used to compute the present value of the investment when you know its future value.

Obviously, this is only a basic example of a compound interest table. In fact, they are usually much, much larger, as they contain more periods t t t various interest rates r r r and different compounding frequencies m m m ... You had to flip through dozens of pages to find the appropriate value of the compound amount factor or present worth factor.

With your new knowledge of how the world of financial calculations looked before Omni Calculator, do you enjoy our tool? Why not share it with your friends? Let them know about Omni! If you want to be financially smart, you can also try our other finance calculators.

Now that you know how to calculate compound interest, it's high time you found other applications to help you make the greatest profit from your investments:

To compare bank offers that have different compounding periods, we need to calculate the Annual Percentage Yield, also called Effective Annual Rate (EAR). This value tells us how much profit we will earn within a year. The most comfortable way to figure it out is using the APY calculator , which estimates the EAR from the interest rate and compounding frequency.

If you want to find out how long it would take for something to increase by n%, you can use our rule of 72 calculator . This tool enables you to check how much time you need to double your investment even quicker than the compound interest rate calculator.

You may also be interested in the credit card payoff calculator , which allows you to estimate how long it will take until you are completely debt-free.

The depreciation calculator enables you to use three different methods to estimate how fast the value of your asset decreases over time.

Tibor Pál, a PhD in Statistical Methods in Economics with a proven track record in financial analysis, has applied his extensive knowledge to develop the compound interest calculator.

Inspired by his own need to calculate long-term investment returns and simplify the process for others, Tibor created this tool. It's designed to help users plan their financial future, whether for retirement, saving for a home, or understanding the potential growth of their investments.

Tibor has extensively used this calculator in various projects, allowing him to project financial outcomes accurately and advise on investment strategies. It's become an essential tool for anyone needing to calculate the future value of their investments, considering different compounding frequencies and additional contributions.

Trust in the compound interest calculator is grounded in our rigorous standards of accuracy and reliability. Financial experts have thoroughly vetted it to ensure it meets the practical needs of both individual investors and financial professionals.

What's compound interest?

Compound interest is a type of interest that's calculated from both the initial balance and the interest accumulated from prior periods. Essentially you can see it as earning interest from interest .

What's the difference between simple and compound interest?

While simple interest only earns interest on the initial balance , compound interest earns interest on both the initial balance and the interest accumulated from previous periods .

How do I calculate compound interest?

To calculate compound interest is necessary to use the compound interest formula , which will show the FV future value of investment (or future balance):

FV = P × (1 + (r / m)) (m × t)

This formula takes into consideration the initial balance P , the annual interest rate r , the compounding frequency m , and the number of years t .

How long does it take for $1,000 to double?

With a compounding interest rate, it takes 17 years and 8 months to double (considering an annual compounding frequency and a 4% interest rate). To calculate this:

Use the compound interest formula:

Substitute the values . The future value FV is twice the initial balance P , the interest rate r = 4% , and the frequency m = 1 :

2P = P × (1 + (0.04 / 1)) (1 × t) 2 = (1.04) t

Solve for time t :

t = ln(2) / ln(1.04) t = 17.67 yrs = 17 years and 8 months

Balance transfer

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Directions: This calc will solve for: A (final amount), P ( principal ) , r ( interest rate ) or T (how many years to compound)

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Simple & Compound Interest Calculator

Our calculator allows the accurate calculation of simple or compound interest accumulated over a period of time.

To use our calculator, simply:

Select the currency from the drop-down list (this step is optional).

Choose what you would like to calculate:

• 1. The simple interest, or
• 2. Compound interest.

Enter the principal amount, interest rate, time period, and click 'Calculate' to retrieve the interest.

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Interest Type: Simple Compound

Compound Frequency: Daily Weekly Monthly Quarterly Annually

Principal Amount :

Annual Interest Rate (%):

Period: Days Weeks Months Quarters Years

Number of Years to Double Investment Chart

Simple interest.

Simple interest is calculated only on the principal amount of an investment.

The following formula can be used to find out the simple interest:

• I = amount of interest, P = principal amount, r = annual interest rate, t = time in years.

Compound Interest

Compound Interest is calculated on the principal amount and also on the interest of previous periods.

The following formula can be used to find out the compound interest:

• A = P×(1 + r/n) nt
• A = final amount including interest, P = principal amount, r = annual interest rate (as decimal), n = number of compounds per year, t = number of years.
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Use our quick and easy tools to calculate Compound Interest. Discover the miracle of compounding.

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Compound Interest Calculator

Enter the values you know. The value left out will be automatically calculated using the formula : $A = P(1 + \frac{r}{n})^{nt}$ and displayed.

Compound Interest Formula

There is a special case when n -> ∞. This is called continuous compounding.

Calculating Other Variables while not continuously compounding ( i.e. when n !-> ∞ )

Calculate principal, calculate rate of interest, calculate time.

Calculating Other Variables while continuously compounding ( i.e. when n -> ∞ )

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Compound Interest Calculator

Determine how much your money can grow using the power of compound interest. 

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Interest Rate Calculator

Free online calculator to estimate the interest rate and total interest cost of an amortized loan with a fixed monthly repayment amount.

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Interest Rate

Interest Rate: 3.74%

Total of 120 Monthly Payments: $120,000.00

Total Interest Paid: $20,000.00

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Table of Contents

What is the interest rate, simple vs. compound interest, fixed vs. variable interest rates, economic policy and inflation, economic activity, unemployment rate, supply and demand, individual credit position, real interest rate, loan specifics, secured loans, borrow when the market is favorable, do not apply for credit too often, do your homework and shop around.

With the interest rate calculator, you can compute the interest rates for loans with fixed terms and monthly payments. Suppose a vehicle dealer provides monthly payment and total price information but does not include the real interest rate. In that case, the calculator can still compute interest rates. Try the Interest Calculator or the Compound Interest Calculator to determine how much interest you’ll earn on an investment.

It is also known as the cost of borrowing money. The interest rate is the amount lenders charge borrowers for using money, expressed as a percentage of the principal, or original loan amount. A yearly interest rate of 8% on a $100 loan means the borrower must pay back $108 at the end of the year.

The interest rate directly affects the total interest paid on the loan. Interest rates can be given in many ways, such as annually, monthly, daily, or at other time intervals. Most people prefer low interest rates because it will cost less to borrow. And lenders (or investors) prefer high interest rates because they can make more money from loans.

Interest rates play a role in practically all formal lending and borrowing transactions. Interest rates include mortgage interest rates, charges on outstanding credit card debt, loans to finance capital projects, pension fund growth, depreciation of long-term assets, price reductions given by a supplier to a customer for paying an invoice early, etc.

You can calculate interest in two ways. Simple interest is calculated only as a percentage of the principal amount owed. When calculating compound interest, we must take all accumulated interest into account. The interest received by creditors is compounded because of this compounding property. The more interest is compounded, the more interest will accrue at a particular time.

We can use compound interest in modern formal interest calculations, including this calculator. And unless otherwise noted, all further references to the interest rate will refer to compound interest.

To calculate values or learn more about compounding frequency changes, use the Compound Interest Calculator .

The interest rate on a loan with a fixed interest rate will never change. Variable rates are the interest rates that change over time. Interest rates, inflation, and stock market indices can affect the variation. The Interest Rate Calculator will only show the outcome as a fixed interest rate, despite each having advantages and disadvantages.

APR (Annual Percentage Rate) is a standard statistic for expressing interest rates on different loans. We often use APRs when buying a home or a car. They differ from standard interest rates in that they might include additional expenses. For example, when purchasing a new automobile, administrative costs are sometimes folded into the financing of the loan rather than paid beforehand. The annual percentage rate can better compare similar products than the interest rate since it provides a more realistic picture of the costs involved.

Annual Percentage Yield, or APY, is the interest rate usually earned on a savings account or certificate of deposit at a financial institution (in the United States). Please visit the APR Calculator for additional information or to do APR calculations.

The Impact of Unpredictable Economic Conditions on Interest Rates

For mortgage and car loan interest rates, several variables come into play. Although most of these factors are beyond our control, we may still benefit from awareness.

A central bank’s monetary policy is the primary factor influencing interest rates in most industrialized countries. Prices of products and services are rising while money’s purchasing power decreases, a phenomenon known as inflation. The primary goal of monetary policy is to keep inflation under control.

Adjustments to interest rates are a powerful macroeconomic tool that can have profound effects on the economy. The Federal Reserve's Federal Open Market Committee (FOMC) gathers several times a year—up to eight—to review and determine the federal funds rate, which influences U.S. interest rates. The FOMC aims to manage inflation and maintain it at a target rate, typically around 2% annually, as part of its dual mandate to foster maximum employment and price stability.

Rising interest rates reduce consumer confidence and the number of people and companies willing to borrow. When interest rates go down in the economy, borrowing money to expand a business, buy a new car, or buy a house becomes more common. This will lead to more employment, higher wages, and consumer confidence in the economy.

Central banks employ interest rates as one of their most important weapons for regulating the economy. Central banks usually decrease interest rates when the economy is weak and raise them when it is growing too quickly.

High unemployment generally leads to decreased consumer spending, which can slow down economic growth. Conversely, low unemployment can stimulate increased spending, potentially driving up wages and business costs, which may lead to inflationary pressures. Consequently, central banks often adjust interest rates in response to changes in the unemployment rate to maintain economic stability.

Typically, central banks may lower interest rates during periods of high unemployment to encourage borrowing and spending, thus stimulating economic activity. Conversely, to prevent the economy from overheating when unemployment is low—which can be indicative of robust consumer spending and economic vitality—interest rates may be increased to moderate spending and keep inflation in check. This reflects the countercyclical role of monetary policy in managing economic fluctuations.

The credit market is determined by supply and demand in the same way as the market for goods and services, although to a lesser extent. Lenders raise interest rates when there is an excess demand for money or credit. Lenders decrease rates to attract more borrowers when there is less demand for credit or money. Banks and credit unions still have to meet their reserve requirements, and there is a maximum amount they can lend.

Controllable Factors Influencing Interest Rates

Even though many things that affect interest rates are hard to predict, people can have some effect on their rates.

Credit scores and reports are available in the United States for lenders to measure risk. The higher a person’s credit score ranges from 300 to 850, the more creditworthy they are as borrowers.

The average credit score of American consumers is 700. Over time, consumers build a good credit score through regular payments, minimal credit use, and other metrics such as credit utilization ratio. If a consumer misses or fails to make payments, has a high credit utilization ratio, has a large total debt, or goes bankrupt, their credit score decreases.

To qualify for better interest rates, you must have a credit rating of at least 750. Those with higher credit scores are likely to get lower interest rates. Low credit scores, bankruptcy, and missed credit card payments make lenders wary of lending money to such applicants. They prefer to lend to people with a spotless record of on-time mortgage and car payments.

Companies either deny or raise interest rates to protect themselves from loan defaults by high-risk borrowers. A credit card firm may raise the interest rate on an account if the customer has a history of missed payments.

The relationship between the real interest rate, inflation, and the nominal interest rate is often approximated by the equation:

Real rate + Inflation = Nominal rate

This formula suggests that the nominal interest rate, the rate commonly referred to in financial contexts, is the sum of the real interest rate (the rate adjusted for inflation) and the expected inflation rate. However, it's important to note that this is a simplification. The more comprehensive Fisher equation, which accounts for the compounding of interest, is given by:

1 + Nominal rate = (1 + Real rate) × (1 + Inflation rate)

For low rates of inflation and interest, the simple addition used in the approximation is generally adequate. Nonetheless, when dealing with higher rates or more precise financial calculations, the full version of the Fisher equation should be employed. For detailed calculations, especially over longer periods or with significant inflation rates, please use the Inflation Calculator, which can give a more accurate analysis.

How to Receive Better Interest Rates

A person's credit history is one of the most important things affecting whether they get reasonable interest rates. But there are other things borrowers should think about as well.

More extended repayment periods are riskier for lenders, resulting in a higher interest rate. The interest rate may decrease if a borrower chooses a shorter loan term and puts down more money. The interest rate can increase for the borrower if the down payment is too low, which is also risky.

Because of the lack of collateral, unsecured loans have higher interest rates than secured loans. Secured loans provide lower interest rates for borrowers who are willing to put up security. If the borrower cannot pay, the lender is entitled to the collateral used as security.

Borrowers cannot change economic conditions but can take out loans when the market is promising. Lower interest rates can be seen when the economy is weak and there is less loan demand.

If a high-risk borrower’s credit report shows a lot of inquiries, it means they may have trouble getting credit. Even a single query might lower your credit score by many points.

Interest rates offered by different lenders vary. Getting a reasonable rate and considering extra costs and conditions is essential. It is quite possible, as a bargaining tool, to announce to each lender that the other is providing a lower rate. A borrower might save money by shopping around for loans rather than taking the first one that comes their way.

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Interest Rate Calculator

The Interest Rate Calculator determines real interest rates on loans with fixed terms and monthly payments. For example, it can calculate interest rates in situations where car dealers only provide monthly payment information and total price without including the actual rate on the car loan. To calculate the interest on investments instead, use the Interest Calculator , or use the Compound Interest Calculator to understand the difference between different interest rates.

Related APR Calculator | Interest Calculator | Compound Interest Calculator

What is Interest Rate?

Interest rate is the amount charged by lenders to borrowers for the use of money, expressed as a percentage of the principal, or original amount borrowed; it can also be described alternatively as the cost to borrow money. For instance, an 8% interest rate for borrowing $100 a year will obligate a person to pay $108 at year-end. As can be seen in this brief example, the interest rate directly affects the total interest paid on any loan. Generally, borrowers want the lowest possible interest rates because it will cost less to borrow; conversely, lenders (or investors) seek high interest rates for larger profits. Interest rates are usually expressed annually, but rates can also be expressed as monthly, daily, or any other period.

Interest rates are involved in almost all formal lending and borrowing transactions. Examples of real-world applications of interest rates include mortgage rates, the charge on a person's outstanding debt on a credit card, business loans to fund capital projects, the growth of retirement funds, amortization of long-term assets, the discount offered by a supplier to a buyer for paying off an invoice earlier, and much, much more.

Simple vs. Compound Interest

There are two methods for calculating interest. Simple interest is calculated as a percentage of principal only, while compound interest is calculated as a percentage of the principal along with any accrued interest. As a result of this compounding behavior, interest earned by lenders subsequently earns interest over time. The more frequently interest compounds within a given time period, the more interest will be accrued. Most formal interest payment calculations today are compounded, including those for this calculator, and any following reference to the interest rate will refer to compound interest rather than simple interest unless otherwise specified. To do calculations or learn more about the differences between compounding frequencies, please visit the Compound Interest Calculator .

Fixed vs. Variable Interest Rates

Fixed rates are rates that are set as a certain percentage for the life of the loan and will not change. Variable rates are interest rates that can fluctuate over time. The degree of variance is generally based on factors such as another interest rate, inflation, or a market index. There are different pros and cons to each, but the Interest Rate Calculator will only display the result as a fixed interest rate.

The interest rate for many types of loans is often advertised as an annual percentage rate, or APR. APRs are commonly used within the home or car-buying contexts and are slightly different from typical interest rates in that certain fees can be packaged into them. For instance, administrative fees that are usually due when buying new cars are typically rolled into the financing of the loan instead of paid upfront. APR is a more accurate representation than the interest rate when shopping and comparing similar competing. On the other hand, annual percentage yield (APY) is the interest rate that is earned at a financial institution, usually from a savings account or Certificate of Deposit (in the U.S.). For more information or to do calculations involving APR, please visit the APR Calculator .

Uncontrollable Economic Factors that Affect Interest Rate

There are many factors that affect what interest rates people get on their mortgages and auto loans. Although these largely cannot be controlled, having knowledge of these factors may still be helpful.

Economic Policy and Inflation

In most developed countries today, interest rates fluctuate mainly due to monetary policy set by central banks. The control of inflation is the major subject of monetary policies. Inflation is defined as the general increase in the price of goods and services and the fall in the purchasing power of money. It is closely related to interest rates on a macroeconomic level, and large-scale changes in either will have an effect on the other. In the U.S., the Federal Reserve can change the rate at most up to eight times a year during the Federal Open Market Committee meetings. In general, one of their main goals is to maintain steady inflation (several percentage points a year).

Economic Activity

In an economy, as interest rates go down, more businesses and people are inclined to borrow money for business expansion and making expensive purchases such as homes or cars. This will create more jobs, push up salary levels, and boost consumer confidence, and more money will be spent within that economy. On the other hand, if interest rates increase, consumer confidence goes down, and fewer people and businesses are inclined to borrow. Based on this, the central bank uses the interest rate as one of the main tools to control the economy. The central bank typically lowers the interest rate if the economy is slow and increases it if the economy expands too fast.

Unemployment Rate

When the unemployment rate is high, consumers spend less money, and economic growth slows. However, when the unemployment rate is too low, it may lead to rampant inflation, a fast wage increase, and a high cost of doing business. As a result, interest rates and unemployment rates are normally inversely related; that is, when unemployment is high, interest rates are artificially lowered, usually in order to spur consumer spending. Conversely, when unemployment within an economy is low and there is a lot of consumer activity, interest rates will go up.

Supply and Demand

Similar to the market for goods and services, the market for credit is determined by supply and demand, albeit to a lesser extent. When there exists a surplus of demand for money or credit, lenders react by raising interest rates. When there is less demand for credit or money, they lower rates in order to entice more borrowers. With that said, banks and credit unions still have to adhere to their reserve requirements, and there is a maximum amount that they can lend out at any time.

Controllable Factors that Determine Interest Rate

While many factors that affect the interest rate are uncontrollable, individuals can, to some degree, affect the interest rates they receive.

Individual Credit Standing

In the U.S., credit scores and credit reports exist to provide information about each borrower so that lenders can assess risk. A credit score is a number between 300 and 850 that represents a borrower's creditworthiness; the higher, the better. Good credit scores are built over time through timely payments, low credit utilization, and many other factors. Credit scores drop when payments are missed or late, credit utilization is high, total debt is high, and bankruptcies are involved. The average credit score in the U.S. is around 700.

The higher a borrower's credit score, the more favorable the interest rate they may receive. Anything higher than 750 is considered excellent and will receive the best interest rates. From the perspective of a lender, they are more hesitant to lend to borrowers with low credit scores and/or a history of bankruptcy and missed credit card payments than they would be to borrowers with clean histories of timely mortgage and auto payments. As a result, they will either reject the lending application or charge higher rates to protect themselves from the likelihood that higher-risk borrowers default. For example, a credit card issuer can raise the interest rate on an individual's credit card if they start missing many payments.

How to Receive Better Interest Rates

Although individual credit standing is one of the most important determinants of the favorability of the interest rates borrowers receive, there are other considerations they can take note of.

• Secured loans —Generally speaking, unsecured loans will carry higher interest rates than secured loans, mainly because there is no collateral involved. That is, if the borrower defaults, the lender is legally entitled to ownership of the collateral. Borrowers seeking more favorable interest rates can consider putting up collateral for a secured loan instead.
• Loan specifics —Longer repayment terms can increase the interest rate because it is riskier for lenders. In addition, making too low a down payment (which is also seen as risky) can result in the borrower receiving a higher interest rate. Choosing a shorter loan term and putting more money down can lower the interest rate a borrower is subject to.
• Do not apply for credit too often —Too many inquiries on a credit report tell a lender that a borrower may have trouble attaining credit, which is a sign of a high-risk borrower. A single inquiry can deduct a few points off a credit score!
• Borrow at opportune moments —While borrowers have no control over economic factors, they can choose to borrow during times when economic factors are more favorable. When the economy is slow and demand for loans is low, it is possible to find lower interest rates.
• Research and shop around —Different lenders have different rates. Borrowers may be able to find a lower interest rate by shopping around rather than accepting the first loan offered. It is possible to reveal to each lender that another is offering a better rate as a negotiation tactic. While getting a good rate is important, be careful about specific conditions and any additional costs.

Real Interest Rate

The relationship between real interest rate, inflation, and the nominal rate is shown by the following equation:

real rate + inflation = nominal rate

In this equation, the nominal rate is generally the figure being discussed when the "interest rate" is mentioned. The nominal rate is the sum of the general level of inflation and the real rate of interest that is being applied. For more information about or to do calculations involving inflation, please visit the Inflation Calculator .