KS4. Number. Interest

If we borrow money from a bank, we normally have to pay interest on the debt. Often, to encourage people to deposit money in a bank, a bank will pay interest to the people that deposit money with them. This interest is calculated as a percentage of the deposit (sometimes called the principal).

We use two methods for calculating interest. Simple interest assumes that the interest is calculated based on a fixed amount which doesn’t change. Compound interest assumes that the interest is added to the principal each year, so the amount on which the interest is calculated does not stay fixed.

Simple Interest

As the name suggests, this is the more straightforward kind of calculation, but applies less often than compound interest (although there are situations where it applies).

We use the formula below to calculate simple interest (write it down), but we must always be very careful to check whether a question is asking for the amount of interest received, or the total amount held (i.e. the original amount plus the interest received):

Example: If $400 is deposited for 6 months at a simple interest rate of 5%p.a., how much interest will be received.

Exercise

Let’s complete exercise 29 from page 104 of the core textbook:

The answers are below:

Compound Interest

Compound interest – the situation where the interest received is added to the principal each year and used to calculate the following years interest – is typically a much more realistic situation. The formula for calculating compound interest is a little more complicated and should be memorised. Again, always check whether we are interested in the total final amount (calculated directly from the formula) or the interest received (in which case we need to subtract the principal):