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.

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Compound Interest Examples (wallstreetmojo.com)

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:

In the present case,

  • A (Future value of the investment) is to be calculatedP (Initial value of investment) = $ 5,000r (rate of return) = 10% compounded annuallym (number of the times compounded annually) = 1t (number of years for which investment is made) = three years

Now, the calculation of future valueCalculation Of Future ValueThe Future Value (FV) formula is a financial terminology used to calculate cash flow value at a futuristic date compared to the original receipt. The objective of the FV equation is to determine the future value of a prospective investment and whether the returns yield sufficient returns to factor in the time value of money.read more (A) can be done as follows.

  • A = $ 5,000 (1 + 0.10 / 1) 1*3A = $ 5,000 (1 + 0.10) 3A = $ 5,000 (1.10) 3A = $ 5,000 * 1.331A = $ 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.

To calculate the value of an investment after five years, the 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 (Future Value of the investment) is to be calculatedP (Initial value of investment) = $ 10,000r (rate of return) = 3% compounded monthlym (number of the times compounded monthly) = 12t (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*5A = $ 10,000 (1 + 0.03 / 12) 60A = $ 10,000 (1.0025) 60A = $ 10,000 * 1.161616782A = $ 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.

To calculate the value of the investment after two years compound interest formula quarterly will be used:

  • A (Future Value of the investment) is to be calculatedP (Initial value of investment) = $ 10,000r (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 quarterlym (number of the times compounded quarterly) = 4 (times a year)t (number of years for which investment is made) = two years

  • A = $ 10,000 (1 + 0.02 / 4) 4*2A = $ 10,000 (1 + 0.02 / 4) 8A = $ 10,000 (1.005) 8A = $ 10,000 * 1.0407A = $ 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.

To calculate the return on an investment after ten years, the compound interest formula will be used:

  • A (Future Value of the investment) = $ 1,600P (Initial value of investment) = $ 1,000r (rate of return) = to be calculatedm (number of the times compounded yearly) = 1t (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 = rr = 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.

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 and 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 charged on the sum of the principal amount and the total interest amassed on it so far. It plays a crucial role in generating higher rewards from an investment.read more, 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.

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 –

  • Power of CompoundingDaily Compound InterestCAGR Formula (Compounded Annual Growth Rate)Continuous Compounding Formula