Eleri invests £3700 for 3 years at 2% per annum compound interest. Calculate the value of her investment at the end of the 3 years. Give your answer correct to the nearest penny.

This question is a classic example of a problem which might catch some students out, if due care is not implemented.

Eleri is investing £3700 at 2% per annum compound interest. This means that the sum of the investment increases by 2% each year.

After the first year, Eleri’s £3700 investment will have grown by 2%, so our first step will be to solve 2% of £3700. Notice that 2% is equivalent to 0.02 in decimal form. Therefore, 2% of 3700 is:

3700 x (0.02) = 74

To deduce the sum of the investment at the end of the year, we add this value (74) to the initial value (3700). Therefore, the sum of the investment at the end of the year is:

3700 + 74 = 3774

We have shown that after one year, Eleri’s investment has increased from £3700 to £3774.

To discover the value of Eleri’s investment after the second year, we repeat the method that we used to discover the value of the investment after one year.

So, 2% of 3774 is:

3774 x (0.02) = 75.48

Therefore, the sum of the investment at the end of the second year is:

3774 + 75.48 = 3849.48

We use the same method to discover the value of Eleri’s investment after the third year.

 2% of 3774 is:

3849.48 x (0.02) = 76.9896

Therefore, the sum of the investment at the end of the third year is:

3849.48  x 76.9896 = 3926.4696

We have found out the value of Eleri’s investment after 3 years of compound interest!

Notice that the question asks for the answer to be correct to the nearest penny. So our final answer to the problem will be:

£3926.47

Note: Once a student is fairly confident it their understanding of a problem such as this, one can discuss methods which are quicker to use, without obscuring what is going on.