## 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 the case of compound interest, interest is earned not only on the 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 below.

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Source: Compound Interest Examples (wallstreetmojo.com)

### 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 three years if the investment earns the return of 10 % compounded monthly.**

**Solution:**

In order to calculate the value of the 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.

### 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 five years if the investment earns the return of 3 % compounded monthly.**

**Solution:**

In order to calculate the value of an investment after the period of 5 years compound interest formula monthlyCompound Interest Formula MonthlyMonthly compound interest refers to the compounding of interest every month, which implies that the compounding interest is charged both on the principal and the accumulated interest.read more 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.

### 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 two years if the investment earns the return of 2 % compounded quarterly.**

**Solution:**

In order to calculate the value of the 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 returnRate Of ReturnRate of Return (ROR) refers to the expected return on investment (gain or loss) & it is expressed as a percentage. You can calculate this by, ROR = {(Current Investment Value – Original Investment Value)/Original Investment Value} * 100read more) = 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.

### 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 a return of 4.81 % compounded yearly with the value of the initial investment of $ 1,000 when sold after a period of 10 years.

### Compound Interest Examples Video

### 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 made where the return is earned using compound interestCompound InterestCompound Interest is the interest earned from the initial Principal & the previously accumulated Interest amount. This is also known as “Interest on Interest” & it is always higher than the Simple Interest. read more, 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 various examples of compound interest – Annually, Monthly, Quarterly. You may learn more about financial modeling from the following articles –

- Power of Compounding
- Daily Compound Interest
- CAGR Formula (Compounded Annual Growth Rate)
- Continuous Compounding Formula

Trudy says

Very helpful. At first I had problems with the formulas, not knowing which formular to use and when to use it. Now am ok. Thanks very much.

Dheeraj Vaidya says

Thanks for your kind words!