A couple is considering buying a house with a mortgage loan of $138,000 and amortization period of 20 years. The annual mortgage interest is currently 5.75% compounded semi-annually. The mortgage is paid back using constant total payments.

(a) Make up the annual mortgage repayment scheme consisting of principal, interest, and repayment and total payment for 20 years. The scheme should be well designed, with appropriate formats.

(b) What is the future value of the annual total payments after 20 years? What is the future value of principal after 20 years? Comment on your result.

(c) If monthly instead of annual payments are made, what is the equivalent monthly payment? What is corresponding yearly payment? Is it more or less than annual mortgage payment calculated in part a)? Why?

(d) For an annual interest rate of 5.75% compounded semi-annually, what mortgage loan can be obtained with constant annual total payments of $12,000 over 20 years? Is it more or less that original mortgage of $138,000? Check your answer by mortgage repayment scheme. Do not use the goal seek function.

(e) For an annual interest rate of 5.75% compounded semi-annually, what mortgage loan can be obtained with constant monthly total payments of $1,000 over 20 years? Is it more or less that original mortgage of $138,000? Do not use the goal seek function.

(f) For what nominal interest rate compounded semi-annually has a loan of $138,000 a monthly payment of $1,000 over 20 years? Is it more or less than original rate of 5.75%? Comment. Hint: Google the "RATE" Excel built-in function and use it to calculate the answer. If you use it correctly for this problem, it returns the monthly interest rate (MIR). Then take necessary steps to convert MIR to its equivalent nominal interest rate compounded semi-annually.

(g) Assume now that the interest rate compounded semi-annually varies every five years, and that in the four five-year periods it is 5.75%, 7.25%, 5.25% and 3.50%. Payments in the first years are made as if the interest rate will be 5.75% during the 20 years, in the second five years as if the interest rate will be 7.25% in the remaining 15 years, and so on. Make up the resulting annual mortgage repayment scheme.