Q$5.$ You are anticipating receiving a stream of monthly cash flows starting at the end of the

fifth month, with the first payment being $$150.$ Each subsequent monthly cash flow will

increase by $0\mathrm{.}5\%$ over the previous month's cash flow. This pattern continues until the end of

the $244$th month, which marks the receipt of the final cash flow. The monthly interest rate

applicable for discounting these cash flows is $0\mathrm{.}5\%.$

a$)$ What is the present value of these cash flows? $[1$ mark$]$

b$)$ What is the future value of these cash flows at the end of ${100}^{th}$ month? $[1$ mark$]$