$\$5000$ is invested at a nominal annual rate of $6\%$, compounded monthly. Find the value after $2$ years, to the nearest cent.
Question HKC78-AIHL-FIN-01
[Maximum mark: 4]
$\$5000$ is invested at a nominal annual rate of $6\%$, compounded monthly. Find the value after $2$ years, to the nearest cent.
Mark Scheme
The monthly rate is $dfrac{0.06}{12} = 0.005$, and there are $24$ months. [1]
Value $= 5000(1.005)^{24}$. [1]
$(1.005)^{24} = 1.1271598ldots$, so the value is $5635.798ldots$. [1]
To the nearest cent, the value is $$5635.80$. [1]
Total: 4 marks
$\$400$ is deposited at the end of each month for $3$ years. The account pays a nominal annual rate of $4.8\%$, compounded monthly. Find the amount in the account immediately after the last deposit, to the nearest dollar.
Question HKC78-AIHL-FIN-02
[Maximum mark: 5]
$\$400$ is deposited at the end of each month for $3$ years. The account pays a nominal annual rate of $4.8\%$, compounded monthly. Find the amount in the account immediately after the last deposit, to the nearest dollar.
Mark Scheme
Monthly rate $i = dfrac{0.048}{12} = 0.004$, and $n = 36$ deposits. [1]
Future value of an ordinary annuity: $400 cdot dfrac{(1.004)^{36} – 1}{0.004}$. [2]
$(1.004)^{36} approx 1.154552$, so the value is $15455.24ldots$. [1]
To the nearest dollar, the amount is $$15455$. [1]
Total: 5 marks
