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.

1. Find the amount allocated to savings using the ratio

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

Savings $=\dfrac{6}{15}\times 35750=14300$

So the principal invested is $\char36{}14300$.

2. Identify the quarterly interest rate and number of compounding periods

Annual rate $=0.25\%$

Quarterly rate $=\dfrac{0.25\%}{4}=0.0625\%=0.000625$

Number of quarters in 2 years $=2\times4=8$

3. Apply the compound interest formula and subtract the principal

Amount after 2 years:

$A=14300(1+0.000625)^8$

Compound interest:

$14300(1.000625)^8-14300=71.656\ldots$

$\text{Compound interest}=\$71.66$