A mortgage for a condominium had a principal balance of $$41,900$ that had to be amortized over the remaining period of $4$ years. The interest rate was fixed at $4\mathrm{.}62\%$ compounded semi$-$annually and payments were made monthly.

a$.$ Calculate the size of the payments.Round up to the next whole number

b$.$ If the monthly payments were set at $$1,057,$ by how much would the time period of the

mortgage shorten? year$($s$)$ months

c$.$ If the monthly payments were set at $$1,057,$ calculate the size of the final payment.Round to the nearest cen