The balance on a mortgage was $$47,500$ and an interest rate of $3\mathrm{.}50\%$ compounded semi$-$annually was charged for the remaining $5-$year term. Monthly payments were made to settle the mortgage.

a$.$ Calculate the size of the monthly payments.

b$.$ If the monthly payments were set at $$964,$ how long would it take to pay off the mortgage?

c$.$ If the monthly payments were set at $$964,$ calculate the size of the final payment.