Simple interest is where each year the interest is calculated by finding the percentage of the initial amount invested.

Find 1.25% of $2000 by dividing 1.25 by 100 to convert to a decimal and then multiplying by the amount.

$\frac{1.25}{100} \times 2000 = 25$

For simple interest, $25 will be the interest for each year.
Find Paddy's amount after 5 years by adding 5 lots of $25 to the initial amount.

$5 \times 25 + 2000 = 2125$

[1]

Compound interest is where each year the interest is calculated by finding the percentage of the current amount.

Recall the formula for compound interest $A = P {(1 + \frac{r}{100})}^{n}$ .
A is the total final amount.
P is the initial amount.
r is the interest rate.
n is the number of years.

Anna's final amount is the same as Paddy's so is also $2125. Substitute A = 2125, P = 2000, n = 5 to form an equation.

$2125 = 2000 {(1 + \frac{r}{100})}^{5}$

Correct right hand side expression [1]
Correct equation [1]

Divide both sides by 2000.

${(1 + \frac{r}{100})}^{5} = \frac{2125}{2000} = 1.0625$

Take the 5th root of both sides.

$1 + \frac{r}{100} = \sqrt[5]{1.0625} = 1.012198 . . .$

[1]

Solve the equation by subtracting 1 from both sides and then multiplying both sides by 100. Use the answer button to avoid losing accuracy.

$\begin{array}{rcl} \frac{r}{100} & = & 0.012198 . . . \\ r & = & 1.2198 . . . \end{array}$

Round to 3 significant figures.

$r = 1.22$ [1]

Simple & Compound Interest, Growth & Decay (CIE IGCSE Maths: Extended)

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