6.4 Simple and compound interest — Learn

Prerequisites: percentage multipliers and repeated multiplication.

Objectives: calculate simple and compound interest. Simple interest adds the same amount each year; compound interest applies the rate to the changing balance.

For simple interest, calculate the yearly interest from the starting amount, then multiply by the number of years. For compound interest, multiply by the yearly growth multiplier each year.

Example 1. Find the final amount for £500 at 4% simple interest for three years.

The yearly interest is £500 × 0.04 = £20.

Three years add £20 × 3 = £60.

The final amount is £500 + £60 = £560.

Example 2. Find the final amount for £500 at 4% compound interest for three years.

The yearly multiplier is 1.04.

£500 × 1.04³ = £562.432.

To the nearest penny, the amount is £562.43.

Watch out. Compound interest does not add the same amount each year. The balance grows, so later interest is calculated from a larger amount. Check that the compound result is above the simple result at a positive rate.

Guided investigation: interest over time

Predict: Which line will be higher after five years at 5%? Test: Move the years control to five. Explain: Why does the gap change each year?

After testing, write why the gap between the balances changes each year.

You should now be able to

• calculate simple interest from the starting amount;
• use a repeated multiplier for compound interest;
• compare the two methods and explain why their totals differ.