Quiz Module 3A

Total: 30 points. No time limit. Counts as participation assessment. Show all work for full credit(use formulae for any calculated cell). Submit one Excel file, start each new problem in a new tab (though you may use more than one tab per question)

5 points for clarity of presentation

[10 pts]The average life ? of a bond is defined as

where PCFt is the principal cash flow at time t, and T is the maturity of the bond.

[1pt.] What is the average life of a zero-coupon bond? Show work

[1pt.] What is the average life of an interest only bond? Show work

[1pt] Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that

where c is the mortgage contract rate.

[7 pts] Compute and graph the average life of a 30 yr. FA FRM in the range of note rates from 2% to 30%. Assume the loan is never prepaid, nor curtailed, nor defaults. Show all work.

[5 pts] A borrower is faced with choosing between two fully amortizing level-payment loans. Loan A is available for $75,000 at 10% MEY for 30 years, with 6 points included in the closing costs. Loan B would be made for the same amount but at 11% MEY for 30 years, with 2 points included in the closing costs. Neither loan defaults/is curtailed.

[4] If the loan is to be repaid after 15 years, which is the better choice?

[2] If the loan is repaid after 5 years, which is the better choice?

Hint: Use the effective cost of borrowing to make the decision. Show work.

[10 pts] A homeowner purchases a property for $1,000,000. She finances the purchase with an 80% LTV, 30-year fully amortizing graduated payment mortgage (GPM) carrying a 10% interest rate. A 20% rate of graduation will be applied to monthly payments beginning year 3 and the beginning of year 5, only (so, fixed for two two-year periods and then fixed for all years 5, 6, 7, ). She will sell the home in year 6. What is the ECB for the loan if the fees are 3% plus $10,000?