Yusuf invests \(\$2000\) at a rate of \(10\%\) per year compound interest. Work out the total interest he earns in 2 years.

Compound interest is applied to the balance at the start of each year, so a rate of \(10\%\) multiplies the amount by \(1.1\) every year.

1. Value after 2 years \(=2000\times 1.1^{2}\) [M1] oe.
2. \(1.1^{2}=1.21\), so the value is \(2000\times 1.21=\$2420\) [M1].
3. The interest earned is the growth on top of the original investment: \(2420-2000=\$420\) [A1] cao.

Year by year the same result appears: \(10\%\) of \(\$2000\) is \(\$200\), giving \(\$2200\) after one year, and \(10\%\) of \(\$2200\) is \(\$220\), giving \(\$2420\). The second year earns \(\$20\) more than the first, and that \(\$20\) is the interest on the first year's interest, which is what compounding means.

Simple interest at the same rate would earn \(2\times\$200=\$400\), so the compound arrangement is \(\$20\) better. The final step matters: the question asks for the interest, not the total value, so \(\$2420\) on its own would not answer it.