Compound Interest

Compound Interest Lesson

Lesson Objectives

Define and explain the concept of compound interest.
Differentiate between simple and compound interest.
Calculate compound interest using the formula.
Solve real-life problems involving compound interest.
Interpret results and analyze the effect of compounding frequency.

Lesson Introduction

Compound interest is all around us—in bank savings, loans, and investments. Unlike simple interest, which is calculated only on the initial principal, compound interest grows over time as interest is added to the original amount. This lesson will help you understand how money can grow faster when interest is compounded over time.

Core Lesson Content

The formula for compound interest is:

$$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$

Where:

$ A $ = Final amount
$ P $ = Principal (initial amount)
$ r $ = Annual interest rate (as a decimal)
$ n $ = Number of times interest is compounded per year
$ t $ = Time in years

Examples

Example 1 (Immediate):
Calculate the amount on ₦10,000 for 2 years at 5% compounded annually.

Given:
$ P = 10000 $, $ r = 0.05 $, $ n = 1 $, $ t = 2 $

A=10000\left(1+\frac{0.05}{1}\right)^{1 \times 2}

=10000(1+0.05)^{2}

=10000 \times(1.05)^{2}

=10000 \times 1.1025

=11025

Final Amount = ₦11,025

Example 2 (Intermediate):
Find the compound interest on ₦8,000 for 3 years at 4% compounded annually.

$ P = 8000 $, $ r = 0.04 $, $ n = 1 $, $ t = 3 $

A= 8000\left(1+\frac{0.04}{1}\right)^{3}

= 8000 \times(1.04)^{3}

= 8000 \times 1.124864

=8998.91

Compound Interest

= A - P = 8998.91 - 8000

= ₦998.91

Compound Interest = ₦998.91

Example 3 (Challenging):
A principal of ₦20,000 is invested for 4 years at 6% compounded quarterly.

$ P = 20000 $, $ r = 0.06 $, $ n = 4 $, $ t = 4 $

A=20000\left(1+\frac{0.06}{4}\right)^{4 \times 4}

=20000(1+0.015)^{16}

=20000 \times(1.015)^{16}

=20000 \times 1.26824

=25364.84

Final Amount = ₦25,364.84

Example 4 (Difficult):
If ₦5,000 is invested at 10% compounded monthly for 2 years, find the compound interest.

$ P = 5000 $, $ r = 0.10 $, $ n = 12 $, $ t = 2 $

A=5000\left(1+\frac{0.10}{12}\right)^{12 \times 2}

=5000(1+0.008333)^{24}

=5000 \times(1.008333)^{24}

=5000 \times 1.2190

=6095.00

Compound Interest = $ 6095.00 - 5000 = 1095.00 $
Compound Interest = ₦1,095.00

Example 5 (Advanced):
What is the rate if ₦15,000 becomes ₦18,000 in 3 years when compounded annually?

$ A = 18000 $, $ P = 15000 $, $ t = 3 $, $ n = 1 $

18000=15000(1+r)^{3}

\frac{18000}{15000}=(1+r)^{3}

1.2=(1+r)^{3}

\sqrt[3]{1.2}=1+r

1.0627=1+r

r=0.0627=6.27 \%

Rate = 6.27%

Exercises

Calculate the amount on ₦12,000 invested for 2 years at 7% compounded annually.
Find the compound interest on ₦25,000 for 3 years at 8% compounded half-yearly.
What will ₦10,000 become in 5 years at 5% compounded annually?
[WAEC] If ₦18,000 amounts to ₦23,328 in 4 years when interest is compounded annually, find the rate. (Past Question)
[NECO] Calculate the compound interest on ₦16,000 for 2 years at 6% compounded quarterly. (Past Question)
[JAMB] How long will it take ₦5,000 to amount to ₦6,653 at 10% compounded annually? (Past Question)
Find the compound interest on ₦50,000 invested at 12% per annum compounded monthly for 1.5 years.
[NABTEC] A sum of money triples in 6 years when compounded annually. What is the interest rate? (Past Question)
Distinguish between simple and compound interest with examples.
Calculate the final amount of ₦30,000 at 9% compounded annually for 3 years.

Conclusion/Recap

Compound interest helps us understand how investments and loans grow over time. It differs from simple interest by calculating interest on both the principal and the accumulated interest. We’ve covered how to compute compound interest and analyzed various types of problems. In our next lesson, we’ll explore the topic of Depreciation and Exponential Decay, which applies similar principles in reverse.