$\$2000$ is invested at $3.5\%$ per year, compounded annually. Find the value of the investment after $4$ years, to the nearest dollar.
Question HKC78-AISL-FIN-01
[Maximum mark: 4]
$\$2000$ is invested at $3.5\%$ per year, compounded annually. Find the value of the investment after $4$ years, to the nearest dollar.
Mark Scheme
Value $= 2000(1.035)^{4}$. [1]
$(1.035)^{4} = 1.147523ldots$. [1]
$2000 times 1.147523ldots = 2295.05ldots$. [1]
To the nearest dollar, the value is $$2295$. [1]
Total: 4 marks
A loan of $\$8000$ is repaid by $5$ equal payments, one at the end of each year. Interest is $6\%$ per year, compounded annually. Find the annual payment, to the nearest dollar.
Question HKC78-AISL-FIN-02
[Maximum mark: 5]
A loan of $\$8000$ is repaid by $5$ equal payments, one at the end of each year. Interest is $6\%$ per year, compounded annually. Find the annual payment, to the nearest dollar.
Mark Scheme
This is an ordinary annuity. With $r = 0.06$ and $n = 5$, the payment is $A = 8000 cdot dfrac{0.06(1.06)^{5}}{(1.06)^{5} – 1}$. [2]
$(1.06)^{5} = 1.3382256ldots$, so $A = 8000 cdot dfrac{0.0802935ldots}{0.3382256ldots} = 1899.17ldots$. [2]
To the nearest dollar, the payment is $$1899$. [1]
Total: 5 marks
