# Compound Interest Examples

Published on :

21 Aug, 2024

Blog Author :

Wallstreetmojo Team

Edited by :

Aaron Crowe

Reviewed by :

Dheeraj Vaidya

## Examples of Compound Interest

In the case of compound interest, interest is earned not only on the principal amount invested initially but also on the interest earned previously from the investment. There are different 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. The following examples of compound interest formulas explain the various situations where the compound interest formula can be used.

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

• Compound interest is when you earn interest not just on your initial money but also on the interest you've already earned.
• Understanding compound interest examples is important as they illustrate how money can grow significantly over time, motivating smart financial decisions and long-term investment planning.
• Interest can compound daily, monthly, quarterly, semi-annually, or annually, determined by the investment terms.
• The compound interest formula is useful for calculating future investment value, rates, etc. It's applicable when interest is earned on both the principal and prior interest.

### Example #1

#### Case of Compounded Annually

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

Solution:

To calculate the value of the investment after three years, the 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 made) = three 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 three 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 five years. Find the value of the investment after the five years if the investment earns a return of 3 % compounded monthly.

Solution:

To calculate the value of an investment after five years, the 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 made) = five 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 five 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 two years. Find the value of the investment after the two years if the investment earns a return of 2 % compounded quarterly.

Solution:

To calculate the value of the investment after two 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 made) = two 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 two 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 ten years, he sold the investment for \$ 1,600 in 2019. Calculate the return on the investment if compounded yearly.

Solution:

To calculate the return on an investment after ten 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 made) = ten years

Now, the rate of return (r) can be calculated 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 ten 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 and previously earned interest part of the investment. In case when the investments are made where the return is earned using compound interest, then this type of investment grows quickly as the interest is earned on the previously earned interest as well; however, one can determine how quickly investment grows only based on the rate of return and number of the compounding periods.

### Frequently Asked Questions (FAQs)

1. Which compound interest investments can earn the most money?

High-yield savings accounts, certificates of deposit (CDs), bonds or bond funds, money market accounts (MMAs), real estate investment trusts (REITs), and dividend-paying equities are among the most lucrative options for compound interest investments.

2. How does compound interest work with stocks?

Compound interest with stocks operates through the compounding of returns over time. When you invest in stocks, your initial investment (principal) grows as you earn returns on it. These returns are reinvested, leading to potential exponential growth. Over time, both your original investment and the accumulated returns generate further returns, creating a compounding effect.

3. What is the relevance of understanding compound interest?

Understanding compound interest is essential because it showcases the power of time and reinvestment in growing your wealth. It is a fundamental concept in finance that demonstrates how small contributions or investments can result in significant accumulations when left to grow over time. This knowledge is relevant not only for personal financial planning but also for making informed investment decisions. Recognizing the potential benefits of compound interest encourages individuals to start investing early, allowing their money to work for them more effectively over the long term.

### Recommended Articles

This has been a guide to Compound Interest Examples. Here we discuss various compound interest examples – Annually, Monthly, and Quarterly. You may learn more about financial modeling from the following articles –