Compound interest

Compound interest is similar to simple interest in that the interest is added on annually.

The difference between the two is that simple interest is a fixed amount of interest that is added on every year. This is based on the original amount.

With compound interest the amount you are calculating interest on, changes every year.

The interest is calculated for the first year and is then added on to the original amount to give the amount after the first year.

The interest for the second year is then calculated from the amount after the first year, which then gives a different amount of interest gained from the first year.

Example

Calculate the amount of compound interest Jane will have earned on £6000 at 2.8% for 3 years.

Method 1

(2.8% can be written as \(\frac{2.8}{100}\) or as 0.028 just as, for example, 34% can be written as \(\frac{34}{100}\) or as 0.34)

Year 1

\(2.8\% \,of\,6000\)

\(= 0.028 \times 6000\)

\(= \pounds168\)

Amount after Year 1:

\(\pounds6000 + \pounds168 = \pounds6168\)

Year 2

\(2.8\% \,of\,6168\)

\(= 0.028 \times 6168\)

\(= \pounds172.70\)

Amount after Year 2:

\(\pounds6168 + \pounds172.70 = \pounds6340.70\)

Year 3

\(2.8\% \,of\,6340.70\)

\(= 0.028 \times 6340.70\)

\(= \pounds177.54\)

Amount after Year 3:

\(\pounds6340.70 + \pounds177.54 = \pounds6518.24\)

Total amount of compound interest earned = \(\pounds6518.24 - \pounds6000 = \pounds518.24\)

Method 2

This is a much quicker method.

As the interest is going up by 2.8% p.a. this means that each year the multiplier is 1.028 (1+2.8% of 1).

\({(1.028)^3} \times 6000\)

\(= \pounds6518.24\)

To find the total amount of interest earned we can subtract the original £6000 from the new total.

Total amount of interest earned = \(\pounds6518.24 - \pounds6000 = \pounds518.24\)

Question

Calculate the compound interest earned on £8000 at 2.2% per annum for 5 years.

Choose the method that you prefer.

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Working with appreciation and depreciationCompound interest