Finance 345 Answers for Chapter 15 Problems on in class exercises
1. List the 5 vital financial features of a mortgage: ___payment,
remaining balance, lender’s yield-irr, borrowers effective borrowing cost
(EBC), Present value of the loan payments.
2. What is the present value of a 30 year loan at 6% interest with 360
level payments of $1,000 each? $166,791.61
3. What would be the fixed level monthly payment on a 15 year 6% loan
of $100,000? $843.86
4. For the loan in problem 3 above what would be the remaining principal
balance on the loan after two payments have been made? $99,310.57
5. For a loan of $100,000 at 7% annual interest for 30 years with equal
monthly payment, what will be the balance of the loan at the end of four
years? $95,474.19
6. What is the lenders yield on the following mortgage: Term 360
months, interest rate 7%, monthly payment $1,000, initial loan balance
$150,307.57, discount points 3.53% : 7.36%
7. Take the loan in 6 above but now look at it from the borrower’s
perspective. In addition to the 3.53% discount points to the lender they
have 3 party loan expenses of $2,692.43 so the net proceeds received by
the borrower is $142,307.57. What are the borrower’s effective borrowing
costs assuming that they hold the loan to maturity? 7.55%
8. Now assume the loan described in 6 and 7 above is paid off by the
borrower in 7 years. Calculate the lender’s yield Ans: 7.68% and the
borrower’s effective borrowing costs: 8.034%
9. A mortgage banker is originating a level payment mortgage with the
following terms: 9% interest, 15 year term, level monthly payment, loan
amount $160,000, discount points to lender$2,000, other upfront costs not
paid to lender $2,000. Calculate lenders yield assuming no prepayment
Ans: 9.22% and borrowers EBC: 9.43%.
10. Assume the loan in 9 is paid off at the end of 7 years. Calculate the
lender’s yield Ans: 9.27% and the borrowers effective borrowing cost
(EBC): 9.56%
11. Suppose a borrower can take out a $250,000 15 year mortgage loan at
4% fixed interest or a 30 year loan at 5% fixed interest and that the
borrower has a large credit card balance at a 12% interest rate (assume that
this is their opportunity cost or discount rate). Assume monthly payments.
Which of these two loans would the household prefer? Ans: 30 year.
Breakeven interest rate is 6.7024% Easy solution is to calc the Payment
under each scenario above and then plug in 12%/12 for the monthly
interest rate and solve for PV. Choose the loan with the lowest PV.
12. Consider a $75,000 mortgage loan with an annual interest rate of 8%,
a loan term of 7 years, but payments based on a 30 year amortization
schedule? Assume monthly payments. What is the balloon payment?
$69,358.07
rd
13. Consider a one-year, $150,000 ARM with a 30-year amortization period. The index rate is
currently 3.75 percent and you estimate that it will increase by 25bp (0.25%) each year for the following
2 years. The fixed margin is 225bp (2.25%), but the lender is offering a teaser rate of 5 percent for the
first year of the mortgage a. Calculate the contract rate, remaining loan balance, and monthly payment
for each of the three years.
b. Suppose that the ARM has a 1 percent annual adjustment cap and an
8 percent overall cap. What is the loan balance and monthly payment for each of the three years?
Beginning of Year
1
2
3
Index
3.75
4
4.25
Margin
2.25
2.25
2.25
Contract rate
5
6.25
6.5
Loan balance
150,000 $147,786.95 $145,921.95
month remaining
360
348
336
Monthly payment -805.232 -920.739
-944.138
Suppose that the ARM has a 1 percent annual adjustment cap and an 8 percent overall cap. The loan
balance and monthly payment for each of the three years: 3?
Beginning of Year
1
2
3
Index
3.75
4
4.25
Margin
2.25
2.25
2.25
Contract rate
5
6.00
6.50
Loan balance
150,000 $147,786.95 $145,836.22
month remaining
360
348
336
Monthly payment -805.232 -897.074
-943.584