You are anticipating receiving a stream of monthly cash flows starting at the end of the fifth month with the first payment being $$100.$ Each subsequent monthly cash flow will increase $0\mathrm{.}5\%$ 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?

b$)$ What is the future value of these cash flows at the end of the $100$th month?