A $$120,000$ mortgage was amortized over $15$ years by monthly repayments. The interest rate on the mortgage was fixed at $5\mathrm{.}30\%$ compounded semi$-$annually for the entire period.

a$.$ Calculate the size of the payments rounded up to the next $$100.$

Round up to the next $100$

b$.$ Using the payment from part a$.,$ calculate the size of the final payment.

Round to the nearest cent