MOnica received a $15$ year loan of $$280000$ to purchase a house. The interest rate on the loan was $4\mathrm{.}30\%$ compounded semi$-$annually. a$)$ What is the size of the monthly loan payment? b$)$ What is the balance of the loan at the end of year $4?$ c$)$ By how much will the amortization period shorten if Monica makes an extra payment of $$30000$ at the end of year $4?$