Martha has just purchased a new house for $$120,000.$ She was able to make a down

payment equal to $25\%$ of the purchase price, and the balance was mortgaged. The rate

quoted by the bank was $10\%$ compounded semi$-$annually. The mortgage has a $20$ year

amortization and five$-$year term.

a$)$ If her payments are made monthly, what are her payments?

b$)$ What will be the balance remaining at the end of the term?

c$)$ Assume that the five years have passed, and the term of the mortgage is up$.$

Martha must now renegotiate her loan. Quoted interest rates are now $12\%.$ Martha

wants to make weekly payments for $15$ years. What are her new payments?