You are planning to borrow $$500,000$ on a $20-$year fully amortized mortgage. The interest rate is

$8\%$ compounded semi$-$annually. You choose the monthly payment.

a$.$ What is the effective monthly rate for calculating the monthly payment? $(1$ point$)$

b$.$ What is your monthly payment? $(1$ point$)$

c$.$ How much will you owe the bank in the end of the $5$th year. $(1$ point$)$

d$.$ What fraction of the payment made at the end of the $12$th year will represent repayment of

principal? $(2$ points$)$