CHAPTER 10
Residential Mortgage Types and Borrower Decisions
Test Problems
1. Private mortgage insurance (PMI) is usually required on _____ loans with
loan-to-value ratios greater than _____ percent.
2. The type of mortgage loan that best fits the asset-liability mix of most depository
institutios is a(n):
3. Which of the following mortgage types has the most default risk, assuming the
initial loan-to-value ratio, contract interest rate, and all other loan terms are
identical?
4. A mortgage that is intended to enable older households to “liquify” the equity in
their home is the:
5. A jumbo loan is:
b. A conventional loan that is too large to be purchased by Fannie Mae or Freddie
6. The maximum loan-to-value ratio for an FHA loan over $50,000 is
approximately:
7. The maximum loan-to-value ratio on a VA guaranteed loan is:
8. Conforming conventional loans are loans that:
9. Home equity loans typically:
10. A simple but durable method of determining whether to refinance is to use:
11. Probably the greatest contribution of FHA to home mortgage lending was to:
Study Questions
1. On an adjustable rate mortgage, do borrowers always prefer smaller (i.e. tighter)
rate caps that limit the amount the contract interest rate can increase in any given
year or over the life if the loan? Explain why or why not.
Solution: Borrowers preferences are influenced by their expectations of future
interest rates. For example, borrowers may prefer wider caps if they believe
2. Explain why a home equity mortgage loan can be a better source of funds for
household needs than other types of consumer debt.
Solution: Unlike interest on consumer debt, interest paid on the first $100,000 of
a home equity loan is fully deductible for federal and, in some cases, state income
3. Distinguish between conforming and nonconforming residential mortgage loans
and explain the importance of the difference.
Solution: Conforming residential loans meet the standards required for purchase
in the secondary market by Fannie Mae or Freddie Mac. Conforming loans have
4. Discuss the role and importance of private mortgage insurance in the residential
mortgage market.
Solution: Private mortgage insurance protects a lender against losses due to
default. Private mortgage insurance companies provide such insurance, which
usually covers the top 20 to 30 percent of loans. In other words, if a borrower
5. Explain the maturity imbalance problem faced by savings and loan associations
that hold fixed-payment mortgages as assets.
Solution: Savings and loan associations historically have used short-term savings
deposits to fund long-term, fixed rate home loans. This mismatch in the maturity
6. Suppose a homeowner has an existing mortgage loan with these terms:
Remaining balance of $150,000, interest rate of 8%, and remaining term of 10
years (monthly payments). This loan can be replaced by a loan at an interest rate
of 6 percent, at a cost of 8% of the outstanding loan amount. Should the
homeowner refinance? What difference would it make if the homeowner expects
to be in the home for only five more years?
Solution a, using net benefit analysis: The payment on the existing loan is
$1,819.91 while the payment on a new loan for the remaining term of ten years
would be $1,665.31. Thus, the new loan results in a monthly savings of $154.61.
Solution b, using net present value (see online chapter appendix): The present
value of the existing loan, with monthly payments of $1,819.91 discounted at 6%,
is $163,925.93. The present value of the new loan is its face value, $150,000. So
7. Assume an elderly couple owns a $140,000 home that is free and clear of
mortgage debt. A reverse annuity mortgage (RAM) lender has agreed to a
$100,000 RAM. The loan term is 12 years, the contract is 9.25%, and payments
will be made at the end of each month.
a. What is the monthly payment on this RAM?
b. Fill in the following partial loan amortization table:
Month Beginning Balance Monthly Payment Interest Ending Balance
1
2
3
4
5
c. What will be the loan balance at the end of the 12-year term?
d. What portion of the loan balance at the end of year 12 represents
principal? What portion represents interest?
Solution:
a. The monthly payment on the RAM is $381.32 (n=144, I=9.25, PV=0,
b. The amortization is as follows:
Month Beginning Balance Monthly Payment Interest Ending Balance
1 0 381.32 0 381.32
2 381.32 381.32 2.94 765.58
d. Principal is 144 x 381.32, or $54,910. Interest is $45,090, or $100,000
8. Eight years ago you borrowed $200,000 to finance the purchase of a $240,000
house. The interest rate on the old mortgage is 6%. Payment terms are being
made monthly to amortize the loan over 30 years. You have found another lender
who will refinance the current outstanding loan balance at 4% with monthly
payments for 30 years. The new lender will charge two discount points on the
loan. Other refinancing costs will equal $6,000. There are no prepayment
penalties associated with either loan. You feel the appropriate opportunity cost to
apply to this refinancing decision is 4%.
a. What is the payment on the old loan?
b. What is the current loan balance on the old loan (five years after
origination)?
c. What should be the monthly payment on the new loan?
d. Should you refinance today if the new loan is expected to be outstanding
for five years?
Solution: (There is an inconsistency in this question as published. Assuming
a. The payment on the old loan is $1,199.10.
b. The current balance is $186,108.71. (after 5 years)
c. The payment on the new loan is $982.35.
d. If the new loan is to be paid off in five more years, the balance of the
Answer based on net benefit analysis:
A new loan at 4 percent with the same term as remains on the original loan
(25 years) would have a payment of $1,000.92. The savings in monthly
Answer based on net present value:
The present value of the old loan, paid off 5 years from today is
The PV of payment reductions is $16,079.10 (202,187.81 – 186,108.71).
The cost of refinancing is $6,000 plus 3,510.89 (0.02 x 186,108.71), or
The NPV of refinancing the loan is $6,356.93 (16,079.10 – 9,722.17).