# How To Solve For Compound Interest

Many students avoid questions involving compound interest. This is often because they do not know the rules and guidelines for solving compound interest. Compound interest is a bit more complex to solve than simple interest, but if you follow the rules, you can deal with it comfortably.

In this article, I will provide detailed step-by-step guidelines for solving questions involving compound interests using several worked examples. By the end of the article, you will be able to handle any arithmetic problem involving compound interest. Ensure that you read to the end.

## What Is Compound Interest?

Compound interest is the interest on a principal that is added to accumulated interests over time. In simple interest, the principal (the amount of money invested) remains the same year after year.

However, in compound interest, the interest you earned in the first year is added to the initial principal invested, which now becomes the principal for the second year of investment. Unlike simple interest, compound interest changes year after year even though the rate is the same.

Commercial banks and big finance houses usually use compound interest. Many loans given to these financial institutions are made with compound interest; therefore, you need to know how to solve it.

## General Formula For Compound Interest

The amount gotten at the end of successive investment years is given by:

A = P ( 1 + R/100)n

Where:

A = Amount

P = Principal

R = Rate

N = number of years

Now, to get our compound interest (C.I), we have to subtract the original principal from this amount

C.I = A – P

But A = P ( 1 + R/100)n

Therefore, C.I = P ( 1 + R/100)n – P

## Worked Examples

Solving compound interest is pretty straightforward. You can calculate it like simple interest, but remember that the interest + original principal in the first year becomes the principal in the second year. We will explain these further using some examples that have been worked on.

### Example 1

Find the C.I on #900 for 3 years at 10% per annum.

#### Solution

C.I = P ( 1 + R/100)n – P

From the question above

P = 900

R  = 10

n = 3

P ( 1 + R/100)n = 900(1 + 10/100)3

= 900 (110/100)3

900(1331/1000)

= 900 (1.331)

A = 1197.9

C.I = 1197.9 – 900

= #297.9

You can still solve this using an alternative method

P = 900

Recall that Simple interest = P x R x T/100

Interest in the Ist year = 900 x 10 x 1/100

= 90

Principal for second year= 900 + 90 = 990

Interest in the second year = 990 x 10 x 1/ 100

= 99

Principal in the third year = 990 + 99 = 1089

Interest for the third year = 1089 x 10 x 1/100

= 108.9

Amount after 3 years = 1089 + 108.9

= 1197.9

C.I = Amount – original P

= 1197.9 – 900

C.I = #297.9

So you can see that whichever way you use, you will still arrive at the correct answer.

### Example 2

Find the C. I on a cassava farm investment of #20, 000 for 2 years at 10% per annum.

#### Solution

You will have to solve to get the amount first

A = P ( 1 + R/100)n

From the question, you are given the following:

P = 20, 000

R = 10

N = 2

A = 20,000 (1 + 10/100)2

= 20,000 (110/100)2

A = 20,000 (121/100)

= 20, 000 x 1.21 = 24, 200

C.I = A – P

= 24, 200 – 20, 000

C.I = #4,200

Try to solve this second example using the alternative method as a personal exercise. You will arrive at the same answer if you follow the steps correctly.

This article has shown you how to solve exercises on compound interest. To master the concept, you should endeavour to solve as many personal exercises as you can. If you have any questions or comments regarding this article, use the comment box below.