Compound Interest

Compound interest is a method of calculating interest where the interest earned is added to the principal amount at the end of each interest period. This leads to a higher interest amount for the next period, as the interest is calculated based on the total amount (principal + interest) at the end of the previous period.

Compound Interest Formula

To calculate compound interest over any number of years, we can use the following formula:

Amount = P(1 + i)^n

where:

  • P = principal amount
  • i = interest rate (as a decimal)
  • n = number of years

Let’s look at an example.

Example: Compound Interest for 10 Years

An amount of £3,600 is deposited into a bank for 10 years at a 0.2% interest rate compounded yearly. How much money will be in the bank after 10 years? Calculate also the interest accrued over the next 10 years.

Amount after 10 years = £3,600(1 + 0.002)^{10} = £3,600(1.002)^{10} = £3,672.65£3,600(1 + 0.002)^{10} = £3,600(1.002)^{10} = £3,672.65 (rounded to 2 decimal places)

Interest accrued over the 10 years = £3,672.65 – £3,600 = £72.65

After 10 years, there will be £3,672.65 in the bank, and the interest accrued over that period will be £72.65.

Comparing Simple and Compound Interest

Let’s look at an example to understand the difference between simple and compound interest. Suppose £1,200 is invested for 3 years at an annual interest rate of 5%.

Simple Interest Calculation:

Simple Interest = (P × R × T) / 100 = (£1,200 × 5 × 3) / 100 = £180

Compound Interest Calculation:

1. Interest at the end of the first year: (1,200 × 5) / 100 = £60 Amount at the end of the first year: £1,200 + £60 = £1,260

2. Interest at the end of the second year: (1,260 × 5) / 100 = £63 Amount at the end of the second year: £1,260 + £63 = £1,323

3. Interest at the end of the third year: (1,323 × 5) / 100 = £66.15 Amount at the end of the third year: £1,323 + £66.15 = £1,389.15

As we can see, compound interest (£189.15) yields a higher return than simple interest (£180) over the same period.

Don’t be puzzled by the division by 100. Keep in mind that 1,200 × 0.05 also equals £60.

You’ve used 0 of your 10 free revision notes for the month

Sign up to get unlimited access to revision notes, quizzes, audio lessons and more

Sign up