This compound interest calculator is a tool which helps you estimate how much money you will earn on your deposit or how your loan or mortgage will grow within a particular period of time. In order to make a smart financial decision, you need to be able to foresee its final results. That's why it's worth knowing how to calculate the compound interest. The most common real-life application of the compound interest formula is a regular savings calculation.

Read on to find answers for the following questions:

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

Interest rate definition

In finance, interest rate is defined as the amount that is charged by a lender to a borrower for the use of assets. Thus, we can say that for the borrower, the interest rate is the cost of debt, and for the lender, it is the rate of return.

Note here that in case you make a deposit in a bank (e.g., put money in your saving account), from a financial perspective it means that you lend 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 (loan outstanding or value of deposit). Usually, it is presented on an annual basis, In that case, it is called the annual percentage yield (APY) or effective annual rate (EAR).

What is the compound interest definition?

First of all, you should find out what compound interest is and how it differs from simple interest. Only then it will be possible to compare these two values.

Generally, compound interest is defined as an interest that is earned not only on the initial amount invested but also on any interest. In other words, compound interest is the interest calculated on the initial principal and the interest which has been accumulated during the consecutive periods as well. 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 compute the value of an investment after a specified period of time or to estimate the rate earned when buying and selling some assets if they are viewed as an investment. It also allows you to calculate some other questions such as the doubling time of investment.

We will show you how to do it in the examples below.

Simple vs. compound interest

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, as we already mentioned, the compound interest is the interest that is calculated on the initial principal plus the interest which has been accumulated.

Compounding frequency

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

For example:

  • annual compounding has a compounding frequency of one
  • quarterly compounding has a compounding frequency of four.
  • monthly compounding has a compounding frequency of twelve.

Note that the greater the compounding frequency is, the greater the final balance.

Compound interest formula

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 under 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:

FV = P (1+ r/m)^mt

Where:

  • FV - the future value of the investment, in our calculator it is the final balance
  • P - the initial balance (the value of the investment)
  • r - the annual interest rate (in decimal)
  • m - the number of times the interest is compounded per year (compounding frequency)
  • t - the numbers of years the money is invested for

How to calculate compound interest

Actually, you don't need to memorize the compound interest formula from the previous section to estimate the future value of your investment. In fact, to do so, you don't even need to know how to calculate compound interest. Thanks to our compound interest calculator you are able to do it within a few seconds. Whenever and wherever you want. (NB: Have you already tried the mobile version of our calculators?)

With our smart calculator, all you need to calculate the future value of your investment is to fill the appropriate fields:

  1. Initial balance - type in the amount of money you are going to invest
  2. Interest rate – provide the interest rate on your investment expressed on a yearly basis
  3. Number of years – type in the number of years you are going to invest money
  4. Compound frequency – in this field you should select the compounding frequency. Usually, the interest is calculated daily, weekly, monthly, quarterly, half-yearly or yearly.

That's it! In a trice, our compound interest calculator makes all necessary computations and gives the results. They are shown in a field final balance where you could see how much you will receive from a deposit after the specified period of time.

Compound interest examples

  • Do you want to understand the compound interest equation?
  • Are you curious how to calculate the compound interest rate in details?
  • 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?

We made the following examples to help you find answers to these questions. We believe that after studying them, you won't have any troubles with the understanding and practical implementation of compound interest.

Example 1 – basic calculation of the value of an investment

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

Data and question

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?

Solution

Firstly let’s determine what values are given, and what we need to find. We know that you are going to invest $10,000 - it is your initial balance P, and the number of years you are going to invest money is 10. Moreover, the interest rate r is equal to 5%, and the interest is compounded on a yearly basis, so the m in the compound interest formula is equal to 1.

What we want to calculate is the amount of money you will receive from this investment. It is the future value FV of your investment.

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

FV = 10,000 * (1 + 0.05/1) ^ (10*1) = 10,000 * 1.628895 = 16,288.95

Answer

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

Your profit will be FV - P. It is $16,288.95 - $10,000.00 = $6,288.95.

Note that when doing calculations you must be very careful about rounding. You shouldn't do too much rounding 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.

Example 2 - complex calculation of the value of an investment

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

Data and question

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?

Solution

Similar to the first example, we should determine the given values first. The initial balance P is $10,000, the number of years you are going to invest money is 10, the interest rate r is equal to 5%, and the compounding frequency m is 12. We need to obtain the future value FV of the investment.

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

FV = 10,000 * (1 + 0.05/12) ^ (10*12) = 10,000 * 1.004167 ^ 120 = 10,000 * 1.647009 = 16,470.09

Answer The value of your investment after 10 years will be $16,470.09.

Your profit will be FV - P. It is $16,470.09 - $10,000.00 = $6,470.09.

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 more during the same period! ($6,470.09 - $6,288.95 = $181.14)

Example 3 - Calculating the doubling time of an investment using the compound interest formula

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 some asset (e.g., property) which you want to see 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 is $2,000 and final balance FV is $3,000. The time horizon of the investment 6 years and the frequency of the computing is 1. This time, we need to compute the interest rate r.

Let's try to plug this numbers in the basic compound interest formula:

3,000 = 2,000 * (1 + r/1) ^ (6*1)

So:

3,000 = 2,000 * (1 + r) ^ (6)

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

3,000 / 2,000= (1 + r) ^ (6)

Raise both sides to the 1/6th power

(3,000 / 2,000) ^ (1 / 6) = (1 + r)

Subtract 1 from both sides

(3,000 / 2,000) ^ (1 / 6) – 1 = r

Finally solve for r

r = 1.5 ^ 0.166667 – 1 = 1.069913 - 1 = 0.069913 = 6.9913%

Answer

In the considered example you earned $1,000 out of the initial investment of $2,000 within the six years. It means 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.

Example 4 - Calculating the doubling time of an investment using the compound interest formula

Let's try something different. 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 closer look at the following example.

Data and question

You put $1,000 on your saving 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.

Solution

The given values are as follows: the initial balance P is $1,000 and final balance FV is 2 * $1,000 = $2,000, and the interest rate r is 4%. The frequency of the computing is 1. The time horizon of the investment t is unknown.

Let's start with the basic compound interest equation:

FV = P (1 + r/m)^mt

Knowing that m = 1, r = 4%, and ‘FV = 2 * P we can write

2P = P (1 + 0.04) ^ t

This could be written as

2P = P (1.04) ^ t

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

2 = 1.04 ^ t

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

ln(2) = t * ln(1.04)

So

t = ln(2) / ln(1.04) = 0.693147 / 0.039221 = 17.67

Answer

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). When using our compound interest rate calculator, however, 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. In such a case just type in any numbers (for example 1 and 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. 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 table

The compound interest tables were used everyday, before the era of calculators, personal computers, spreadsheets, and unbelievable solutions provided by the 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 how a compound interest table looks like.

Basing on the data provided in the compound interest table you are able to calculate the final balance of your investment. All you have to know is that the column compound amount factor shows the value of the factor (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, it is only the basic example of the compound interest table, in fact, they are definitely larger, as they contain more periods t various interest rates r and different compounding frequencies m... Usually, you had to flip dozens of pages to find the appropriate value of compound amount factor or present worth factor.

So… Knowing 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.

Additional Information

Now that you know how to calculate compound interest, it's high time to find other applications which will help you make the greatest profit from your investments. The compound interest equation is not the only thing you should be familiar with.

To compare bank offers which 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 compound interest rate calculator.

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

Another interesting calculator is our cap rate calculator which determines the rate of return on your real estate property purchase.

And finally, why not to try our dream come true calculator. which answers the question: how long do you have to save to afford your dream?

Tomasz Jedynak, PhD, Mateusz Mucha and James Mathison

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Compound Interest Calculator And Formula