A couple is considering buying a house with a mortgage loan of $500,000 and a term of 25 years. The mortgage interest is currently 2.75%. The mortgage is paid back using a constant annual amount for interest and repayment. All interest rates in this question are annual with semi-annual compounding.

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

2. If bi-weekly instead of annual payments are made, what is the equivalent bi-weekly payment? What is corresponding yearly payment? It is more or less that the yearly payment from part 1). Comment.

3. What is the future value of all bi-weekly payments after 25 years? Is it more or less than $500,000? Why?

4. For an annual interest rate of 2.75%, what mortgage loan can be obtained with constant bi-weekly payments of $1,000 over 25 years? Why it is more or less than $500,000?

5. For an annual interest rate of 2.75%, what mortgage loan can be obtained with constant annual payments of $26,000 over 25 years? Why your answers are different in 4) and 5) even though you make the same annual payment of $26,000?

6. For what interest rate has a loan of $500,000 a bi-weekly payment of $1,000 over 25 years? Is it more or less than original 2.75%? Comment!

7. Assume now that the interest rate varies every five years, and that in the four five-year periods it is 2.75%, 3.00%, 2.25%, 2.50% and 2.75%. Payments in the first years are made as if the interest rate will be 2.75% during the 25 years, in the second five years as if the interest rate will be 3.00% in the remaining 20 years, and so on. Make up the resulting annual mortgage repayment scheme.