Naomi received a commission of $35 750 from the sale of a house. This sum of money was divided among his expenditure, insurance premiums and savings in the ratio 5 : 4 : 6. The savings is invested at a rate of 0.25% per annum compounded quarterly for a period of 2 years. Calculate the compound interest earned. Answer $ ...

1. Calculate the amount allocated to savings

Total parts = $5 + 4 + 6 = 15$

$\text{Savings} = \frac{6}{15} \times 35750 = \char36{}14300$

2. Calculate the total amount after 2 years with quarterly compounding

Rate per quarter = $\frac{0.25\%}{4} = 0.0625\%$
Number of quarters = $2 \times 4 = 8$

$\text{Total Amount} = 14300 \left(1 + \frac{0.0625}{100}\right)^8$
$= 14300(1.000625)^8$
$\approx 14371.6564$

3. Calculate the compound interest earned

$\text{Compound Interest} = 14371.6564 - 14300 = 71.6564$
$\approx \char36{}71.66$ (to 2 d.p.)