Financial Mathematic

A mortgage borrower wishes to borrow $550,000, to be repaid over a period of 20 years by fixed monthly instalments. The interest rate (nominal) is 6 per cent per annum, compounded monthly. The first payment is due at the end of the first month.

Required:

a.Calculate the effective annual rate?

b.Calculate the monthly payment to repay the loan?

c.Suppose now that the borrower decides to repay $5000 per month from the time the money is borrowed until it is repaid. How long would it take to repay the loan?

d.Now assume it is 10years later and you have just made a normal payment to the bank. Suppose the bank increases the interest to 6.5% p.a. If the loan term remains the same, what is the new monthly payment?

e.Instead of payingnew monthly payment in point (d), the borrower will continue to pay $5000 monthly payment(point c).How long would it take to repay the loan?