Scenario

You have inherited $$50,000$ and are considering various investment options over a period of $10$ years.

During this period, interest rates and compounding frequencies are expected to change. Your goal is to

determine the best investment strategy to maximize the return on your investment.

Part A: Initial Investment Analysis $(10$ Marks$)$

Initial Investment with Simple Interest $(3$ Marks$)$

For the first $3$ years, you decide to invest your money in a bond that offers a simple

interest rate of $5\%$ per annum.

$($a$)$ Calculate the amount of interest earned and the total amount after $3$ years.

$($b$)$ Formula used and calculation steps $(1\mathrm{.}5$ Marks$)$

$($c$)$ Final interest earned and total amount $(1\mathrm{.}5$ Marks$)$

Part B: Change in Investment Strategy $(15$ Marks$)$

Mid$-$Term Investment with Compound Interest $(7$ Marks$)$

After the initial $3$ years, you decide to reinvest the total amount into a savings account

that offers a compound interest rate of $4\%$ per annum, compounded semi$-$annually, for

the next $4$ years.

$($a$)$ Calculate the future value of the investment after $4$ years.

$($b$)$ Formula used and calculation steps $(3$ Marks$)$

$($c$)$ Final amount $(4$ Marks$)$

Final Investment with Variable Interest Rates $(8$ Marks$)$

For the remaining $3$ years, you switch your investment to a mutual fund that offers a

variable interest rate. The rate is $3\%$ per annum, compounded quarterly for the first

year, and $6\%$ per annum, compounded monthly for the remaining $2$ years.

$($a$)$ Calculate the future value of the investment after the first year at $3\%$ per annum,

compounded quarterly.

$($b$)$ Calculate the future value of the investment for the next $2$ years at $6\%$ per annum,

compounded monthly, starting with the amount from the previous step.

$($c$)$ Formula used and calculation steps $(4$ Marks$)$

$($d$)$ Final amount $(4$ Marks$)$