# 1. [14 pts] a fully amortizing cpm for \$100,000 is made at 8% mey

1. [14 pts] A fully amortizing CPM for \$100,000 is made at 8% MEY for 20 years
a. [2] Calculate the monthly payment.
b. [2] Assume the loan is repaid at the end of 8 years. What is the outstanding balance?
c. [4] Produce an amortization sheet, annotate it. See instructions above.
d. The borrower chooses to curtail the loan by \$5,000 at the end of year 5.
i. [3] What will be the new loan maturity, assuming the payments do not change?
ii. [3] Assume the loan maturity will not change. What are the new payments?

2. [9 pts] John wants to buy a property for \$105,000 and wants an 80% loan. The lender indicates that a fully amortizing loan can be obtained for 30 years at 12% MEY, with loan origination fees of \$3,500.
a. [1] How much will the lender actually disburse?
b. [3] What is the effective interest cost to the borrower, assuming that the mortgage is paid off after 30 years?
c. [1] What is the annual percentage rate (APR) that the lender must disclose to the borrower? (APRs are rounded to the nearest 1/8th of a percent)
d. [2] If John pays off the loan after 5 years, what is the effective interest charge? Why is it different from the APR in c?
e. [2] Assume the lender also imposes a prepayment penalty of 2% of the outstanding balance if the loan is repaid within the first 8 years of closing. What is the effective cost of the loan if John repays after 5 years?

3. [6] A borrower is faced with choosing between two 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 for 11% MEY for 30 years, with 2 points included in the closing costs. Both loans would be fully amortizing.
a. [4] If the loan is to be repaid after 15 years, which is the better choice?
b. [2] If the loan is repaid after 5 years, which is the better choice?

4. [12] A reverse annuity mortgage is made with a balance not to exceed \$300,000 on a property now valued at \$700,000. The loan calls for monthly payments to be made to the borrower for 120 months at an interest rate of 11% MEY.
a. [3] What will the monthly payments be?
b. [3] What will the RAM balance be at the end of year 3?
c. [4] Assume that the borrower must have monthly draws of \$2,000 for the first 50 months of the loan. The remaining draws from months 51 to 120 must be determined so that the \$300,000 maximum is not exceeded in month 120. What will the draws by the borrower be during months 51 to 120?
d. [2] Suppose property experiences a 1% appreciation (MEY, starting today), and the borrower has a balance of \$300,000 at year 10 (by receiving payments computed in a). No payments are made thereafter. How many years from loan closing will the loan balance begin to exceed the house value?

5. [5] Refer to question 4, part d. The fact that healthy borrowers with longer expected lives, or individuals that do not expect to move, are more attracted to RMs than the opposite type of individuals is called “adverse selection” (the lender will tend to get the “worst kind” of borrower, from her point of view).

Go to www.ssrn.com, under “Search,” look for terms “Reverse Mortgage” with author “Davidoff.” Download the paper on selection and moral hazard. The authors have found that in the last 15 years, lenders have experienced “positive selection” (the opposite of adverse selection), in that RM borrowers have tended to leave their homes faster than the population average. What is their proposed explanation for this puzzling result, and can you think of an alternative one?

6. [5] Download the paper “Measuring Housing Affordability…,” by Davidson and Levin which was posted along with this HW document on BB. Discuss why the authors disagree with the NAR about the affordability of homeownership as of the date of the article.

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