## Examples of Compound Interest

The following examples of compound interest formula provide an understanding of the various types of situations where the compound interest formula can be used. In case of compound interest, interest is earned not only on principal amount which is invested initially but it is also earned on the interest earned previously from the investment. There are a different number of periods for which the compounding of the interest can be done which depends on the terms and conditions of the investment like compounding can be done on a daily, monthly, quarterly, semi-annually, annually basis, etc.

We can now see some of the different types of compound interest formula examples as below.

### Example #1

#### Case of Compounded Annually

**Mr. Z makes an initial investment of $ 5,000 for a period of 3 years. Find the value of the investment after the 3 years if the investment earns the return of 10 % compounded monthly.**

**Solution:**

In order to calculate the value of investment after the period of 3 years annual compound interest formula will be used:

**A = P (1 + r / m)**

^{mt}In the present case,

- A (Future value of the investment) is to be calculated
- P (Initial value of investment) = $ 5,000
- r (rate of return) = 10% compounded annually
- m (number of the times compounded annually) = 1
- t (number of years for which investment is done) = 3 years

Now,the calculation of future value (A) can be done as follows

- A = $ 5,000 (1 + 0.10 / 1)
^{1*3} - A = $ 5,000 (1 + 0.10)
^{3} - A = $ 5,000 (1.10)
^{3} - A = $ 5,000 * 1.331
**A = $ 6,655**

Thus it shows that the value of the initial investment of $ 5,000 after the period of 3 years will become $ 6,655 when the return is 10 % compounded annually.

### Compound Interest Formula Example #2

#### Case of Compounded Monthly

**Mr. X makes an initial investment of $ 10,000 for a period of 5 years. Find the value of the investment after the 5 years if the investment earns the return of 3 % compounded monthly.**

**Solution:**

In order to calculate the value of investment after the period of 5 years compound interest formula monthly will be used:

**A = P (1 + r / m)**

^{mt}In the present case,

- A (Future Value of the investment) is to be calculated
- P (Initial value of investment) = $ 10,000
- r (rate of return) = 3% compounded monthly
- m (number of the times compounded monthly) = 12
- t (number of years for which investment is done) = 5 years

Now,the calculation of future value (A) can be done as follows

- A = $ 10,000 (1 + 0.03 / 12)
^{12*5} - A = $ 10,000 (1 + 0.03 / 12)
^{60} - A = $ 10,000 (1.0025)
^{60} - A = $ 10,000 * 1.161616782
**A = $ 11,616.17**

Thus it shows that the value of the initial investment of $ 10,000 after the period of 5 years will become $ 11,616.17 when the return is 3 % compounded monthly.

### Compound Interest Formula Example #3

#### Case of Compounded Quarterly

**Fin International Ltd makes an initial investment of $ 10,000 for a period of 2 years. Find the value of the investment after the 2 years if the investment earns the return of 2 % compounded quarterly.**

**Solution:**

In order to calculate the value of investment after the period of 2 years compound interest formula quarterly will be used:

**A = P (1 + r / m)**

^{mt}In the present case,

- A (Future Value of the investment) is to be calculated
- P (Initial value of investment) = $ 10,000
- r (rate of return) = 2% compounded quarterly
- m (number of the times compounded quarterly) = 4 (times a year)
- t (number of years for which investment is done) = 2 years

Now,the calculation of future value (A) can be done as follows

- A = $ 10,000 (1 + 0.02 / 4)
^{4*2} - A = $ 10,000 (1 + 0.02 / 4)
^{8} - A = $ 10,000 (1.005)
^{8} - A = $ 10,000 * 1.0407
**A = $ 10,407.07**

Thus it shows that the value of the initial investment of $ 10,000 after the period of 2 years will become $ 10,407.07 when the return is 2% compounded quarterly.

### Compound Interest Formula Example #4

#### Calculation of rate of return using Compound Interest Formula

**Mr. Y invested $ 1,000 during the year 2009. After the period of 10 years, he sold the investment for $ 1,600 in the year 2019. Calculate the return on the investment if compounded yearly.**

**Solution:**

In order to calculate the return on an investment after the period of 10 years, the compound interest formula will be used:

**A = P (1 + r / m)**

^{mt}In the present case,

- A (Future Value of the investment) = $ 1,600
- P (Initial value of investment) = $ 1,000
- r (rate of return) = to be calculated
- m (number of the times compounded yearly) = 1
- t (number of years for which investment is done) = 10 years

Now, the calculation of the rate of return (r) can be done as follows

- $ 1,600 = $ 1,000 (1 + r / 1)
^{1*10} - $ 1,600 = $ 1,000 (1 + r)
^{ 10} - $ 1,600 / $ 1,000 = (1 + r)
^{ 10} - (16/10)
^{1/10}= (1 + r) - 1.0481 = (1 + r)
- 1.0481 – 1 = r
**r = 0.0481 or 4.81%**

Thus it shows that Mr. Y earned return of 4.81 % compounded yearly with the value of the initial investment of $ 1,000 when sold after the period of 10 years.

### Conclusion

It can be seen that the compound interest formula is a very useful tool in calculating the future value of an investment, rate of investment, etc using the other information available. It is used in case the interest is earned by the investor on principal as well as previously earned interest part of the investment. In case when the investments are done where the return is earned using compound interest then this type of investment grow quickly as the interest is earned on the previously earned interest as well however one can determine how quickly investment grows only on the basis of the rate of return and number of the compounding periods.

### Recommended Articles

This has been a guide to Compound Interest Examples. Here we discuss how to calculate compound interest (Annually, Monthly, Quarterly) using its formula along with practical examples. You may learn more about financial modeling from the following articles –

- Explanation of Compounding Formula
- Interest Formula Calculator
- Power of Compounding with Examples
- Daily Compound Interest
- CAGR Formula (Compounded Annual Growth Rate)
- Compound Interest Formula in Excel
- Continuous Compounding Formula

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