A couple is considering buying a house with a mortgage loan of $375,000 and a term of 25 years. The fixed annual mortgage interest rate is currently...

A couple is considering buying a house with a mortgage loan of $375,000 and a term of 25 years. The fixed annual mortgage interest rate is currently 5.8%, compounded monthly. The mortgage is paid back using constant total payments.

i. Make up the annual mortgage repayment scheme consisting of principal, interest, repayment and total payment (cashflow) for 25 years. The scheme should be well designed, with appropriate formatting.

ii. What is the future value of the annual total payments after 15 years? What is the future value of principal after 15 years? What is the difference? 

iii. If monthly instead of annual payments are made, what is the equivalent monthly payment? What is corresponding weekly payment?

iv. If you compare the annual payment to twelve times the monthly payment and fifty-two times the weekly payment are they all identical? Which one is the largest? Which one is the smallest? Why are they different?

v. For an annual interest rate of 3.5%, what mortgage loan can be obtained with constant monthly total payments of $1,400 over 25 years?

vi. Assume now that the interest rate varies every five years, and that in the five, five-year periods, it is 5.8%, 5%, 5.5%, 4.9%, and 5.3% compounded annually. Payments in the first years are made as if the interest rate will be 5.8% during the 25 years, in the second five years as if the interest rate will be 5% in the remaining 20 years, and so on. Make up the resulting annual mortgage repayment scheme.