Compound interest is the interest paid on a borrowed amount added to the accumulated interest. An example of compound interest is savings account interest

There is a slight difference between simple interest and compound interest. For simple interest, the interest is calculated and paid at the end of each year and the principle i.e, the amount lent or borrowed does not change.

Under compound interest, the interest is not paid to the lender, instead it is added to the principal at the end of the time (i.e either year, half year, month etc).

For compound interest, the total amount at n year end becomes.

A = P (I + R/100)^{n}

And compound interest

= A – P

Where is the principal

R = rate per annum

n = number of years

Make sure you solve the formula and memorize it because we are going to use it throughout the lesson

### Solution To Compound Interest Questions

**Example 1:**

Find the compound interest on N450 in 4 years at 6% per annum

Solution

Given P = N450, n = 4 years R = 6%

Let calculate the amount first

A = p(I + R/100)^{n}

Substituting the values we have,

A = 450(1 + 6/100)

A = 450 (1+0.06)^{4}

A = 450 (106)^{4}

A = 450 x 1.262

A = N568.11

Therefore, the compound interest = Amount – principal after 4 years

= 568.11 – 450

= N118.11

### Example 2:

A man solved N1000 calculate the amount if the interest rate is 4.2% compounded quarterly

**Solution**

The interest will be calculated base on the different quarter of the year

That is 4 quarters

We use the formula for simple interest here

i.e interest I = principal x rate x time/100

I = P x R x T/100

So for interest earned in the 1^{st} quarter

P = N1,000, R = 42%

Let substitute

I = 1000 x 42 x 1/100

I = N10.50

For interest earned in the 2^{nd} quarter of the year, the interest I of the first year is added to N1000 to obtain the principal for the second quarter

So the interest earned in the 2^{nd} quarter

I = 10.50 + 1000 x 4.2 x 1/100

I = 1010.50 x 4.2 x 1/100

I = N10.61

Interest earned in the 3^{rd} quarter

I = 10.50 + 10.61 + 1000 x 4.2 x 1/100

I = 1021.11 x 4.2 x 1/100

I = 10.72

Interest earned in the 4th quarter

I = 10.50 + 10.61 + 10.72 + 1000 x 4.2 x 1/100

I = N10.83

Therefore, the amount that has accumulated in the account after 4 quarters or 1 year

= 10.30 + 10.61 + 10.7r + 1000 + 10.83

= 1031.83 + 10.83

= 1042.66

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### Example 3:

Find the compound interest on N9000 in 3 years at 4% per annum

Solution

Given, P = N9000, n = 3years

Rate (R) = 4%

Let calculate Amount first

A = P (I + R/100)^{n}

Let substitute into the formula

A = 9000 (I + 4/100)^{3}

A = 9000 ( I + 0.04)^{3}

A = 9000 (1.04)^{3}

A = 9000 x 1.125

A = N10124

Compound interest

= Amount – principal

= 10124 – 9000

N1,124

Therefore, the compound interest is N1,124.

In conclusion, interest follows a set rule which is the use of the formula for the amount and then subtract the principal from the amount to obtain the compound interest required.

Compound interest problems are always straight forward when you follow the rule. It is as easy as that!