Cumulative increase and decrease

Simple interest

With simple interest the amount of money borrowed remains fixed.

For example \pounds400 is borrowed for three years at an interest rate of 5\% per annum.

(per annum means each year)

Interest for one year  = 5\%\,of\,\pounds400

=\frac{5}{100} \times 400

= \pounds20

Interest for 3 years = 20 \times 3 = \pounds60

You can write this in an expression:

P\times R\times T

P (principal) is the amount borrowed.

R is the rate of interest per year.

T is the time in years.

Compound interest

Here the interest is added to the principal at the end of each year. So the next year the interest is worked out on a larger amount of money than what was originally borrowed.

This means paying interest on the interest of previous years (unlike simple interest, where you only pay interest on the original amount).

This is how it is calculated:

\pounds400 is borrowed for three years at 5\% compound interest.

Principal at the start = \pounds400

Interest in the 1st year = \frac{5}{{100}} \times 400 = \pounds20

Principal after 1 year = \pounds420

Interest in the 2nd year = \frac{5}{{100}} \times 420 = \pounds21

Principal after 2 years = \pounds441

Interest in the 3rd year = \frac{5}{{100}} \times 441 = \pounds22.05

Principal after 3 years = \pounds463.05

The total interest charged under compound interest will be \pounds63.05.

This is different to the simple interest worked out above.