Interest is the extra money earned on savings or paid on loans. There are two main types of interest: simple interest and compound interest. The key difference is how the interest is calculated over time.

With simple interest, the interest is calculated only on the original amount of money, called the principal. The interest earned each year is the same.

For example, if £500 is invested at an interest rate of \( 4\% \) per year for 3 years, the interest for one year is:

$$
500 \times 0.04 = 20
$$

Over 3 years, the total interest is:

$$
20 \times 3 = 60
$$

So the final amount is:

$$
500 + 60 = 560
$$

With compound interest, the interest is calculated on the original amount and on any interest already added. This means the amount increases by a larger amount each year.

Compound interest calculations are often done using a multiplier. A multiplier is found by adding the interest rate to 1. For an increase of \( 4\% \), the multiplier is:

$$
1.04
$$

Using the same £500 invested for 3 years with compound interest, the calculation is:

$$
500 \times 1.04^3
$$

$$
= 500 \times 1.124864
$$

$$
= 562.43
$$

So the final amount is £562.43, which is more than with simple interest.

The difference between simple and compound interest becomes more noticeable over longer periods of time. Compound interest grows faster because interest is earned on previous interest.

Using multipliers is an efficient method for compound interest, especially for calculations over several years. Always check whether a question involves simple or compound interest before choosing the method to use.