Compound Interest is the amount of money earned on a sum that has been invested including the interest added each year.

It is usually written as a percentage of the money invested for each year (per annum or p.a.)

**Example 1
**

Jack invests £250 at 1.5% compound interest p.a.

How much compound interest is earned after three years?

**Answer**

When we increase something by 1.5%, we can use the percentage multiplier 1.015.

After 1 year, Jack has £250 x 1.015 = £253.75

After 2 years, Jack has £253.75 x 1.015 = £257.55625

After 3 years, Jack has £257.55625 x 1.015 = £261.41959...** ≈ £261.42
**

Compound interest earned = £261.42 - £250 = **£11.42**

**Example 2
**

Jack invests £250 at 1.5% compound interest p.a.

How much compound interest is earned after ten years?

**Answer**

When we increase something by 1.5%, we can use the percentage multiplier 1.015.

After 1 year, Jack has £250 x 1.015 = £253.75

After 2 years, Jack has £250 x 1.015² = £257.55625

After 3 years, Jack has £250 x 1.015³ = £261.41959...

After 10 years, Jack has £250 x 1.015¹º = 290.1352...

Interest earned = £250 x 1.015¹º - £250 ≈ **£40.14**