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 advisers 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. However, even when the frequency is unusually high, the final value can’t rise above a particular limit. To see this, you may check the natural logarithm, where we explain its background.

### 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

It is worth to know, that when the compounding period is one (`m = 1`

)m then the interest rate (`r`

) is call the CAGR (compound annual growth rate).

### 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:

**Initial balance**– type in the amount of money you are going to invest**Interest rate**– provide the interest rate on your investment expressed on a yearly basis**Number of years**– type in the number of years you are going to invest money**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.

### 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.