Name ________________________________
Adjustable Rate Mortgage
Practice Problems
Use the following information to answer the questions. This ARM has restrictions on the
contract rate movement but no negative amortization.
Loan $165,000
Maturity 30 Years
r(0) 4.20%
m 2.50%
alpha 1.00%
y 1.25%
L 4.00%
Points 1
Future Index Rate:
r(1) 5.30%
r(2) 8.00%
r(3) 7.50%
r(4) 9.25%
r(5) 10.00%
1. What are the yearly contract rates over the next 6 years?
Year
1
2
3
4
5
6
c(i)
5.70%
6.95%
8.20%
9.45%
9.70%
9.70%
2. What is the payment in the 2nd year?
$1,089.20
3. What is the effective borrowing cost if the mortgage is prepaid at the end of the 6th
year?
8.2708%
4. Ignore the future index rates. What is the lowest payment that can occur during the
second year?
$833.92
Name ________________________________
Refinancing Decisions
Practice Problems
Use the following information to answer the questions. This practice problem will help
you prepare for any refinancing questions on the exam. You have been paying five years
on a mortgage with the following terms: Initial Balance - $125,000, contract rate of 10%,
30 yr initial term paid monthly, 3% prepayment penalty, 3 front end points. You are
considering refinancing with a new mortgage which has the following terms: contract rate
of 7%, 25-year term paid monthly, 2 points, 4% prepayment penalty. Further, assume
that any prepayment penalties and points/fees are rolled into the new mortgage when you
initially refinance.
1. What is the beginning balance of the new loan?
$126,826.23
2. What is the monthly savings (benefit) between the old and new loans?
$200.58
3. What are the savings (benefits) in amortization for refinancing under these terms,
assuming you prepay after 2 years?
-$5,856.72
4. What is the NPV of refinancing under the terms given, assuming you hold both
mortgages to maturity?
$28,379.44
[Simply discount the benefit from #2 ($200.58) for 300 months at 7% (the current mortgage rate)]
5. What is the NPV of refinancing under the terms given, assuming you prepay the new
mortgage after 2 years?
-$613.69
Name ________________________________
Incremental Financing and Junior Mortgage
Practice Problems
1. You can borrow 95% of the purchase price at a rate of 6.75%. You can borrow 80%
of the purchase price at 6.25%. What is the incremental cost of borrowing? Assume
monthly payments for 30 years.
9.27%
2. Mr. Davis is assuming a mortgage of $95,000 that has a contract rate of 5.75% and 15
years until maturity. In addition, he is taking out a second mortgage for $30,000 at
9%. The second mortgage also has a 15 year term. What is the combined borrowing
cost? Payments occur monthly.
6.56%
3. To purchase our home we have decided to choose an 80-10-10 mortgage with
monthly payments. The 80% loan is for 30 years and has a contract rate of 6.75%.
The 10% loan is for 15 years and has a contract rate of 9%. What is the lenders’
combined yield? The purchase price is $150,000
6.92%
Name ________________________________
Cash Equivalency
Practice Problems
1. A seller offers zero percent financing for 15 years and nothing down on a home that
has a price of $150,000. Fifteen-year mortgage rates are 7% in the current market
(assuming a 100% LTV). What is the cash equivalent price of this home?
$92,713
2. Mrs. Sellers is selling her home with an assumable mortgage. The balance on the
assumable loan is $130,000. The contract rate is 4.5% and there are 180 remaining
monthly payments. The current market rate on a 15-year loan is 9%. How much
should she increase the asking price in order to capitalize the value of the assumable
mortgage?
$31,950.18
3. You are looking at purchasing a small industrial building the building currently is
offered for sale at $1,875,000 with special financing arranged by the seller. The seller
is offering the property at 5.5% amortized over 15 years assuming a down payment of
20% is included up front. A balloon payment will be required in 5 years. Assuming
you go to the bank and take out a mortgage with the same terms (except the banks
interest rate is 7%), what should you be willing to pay for the property?
$1,790,604
Name ________________________________
Negative Amortization
Practice Problems
Use the following information to answer the questions. This GPM has restrictions on
change in payment and negative amortization occurs at intervals. The adjustment term is
for 6 years with a 30 year amortization.
Loan Balance
Interest Rate
Term in Years
$120,000
9.00%
30
Initial Payment
Allowed Payment Increase
1)
$800.48
5.00% per year
What is the GPM payment in year 2?
$840.50
2)
What is the change in loan balance in year 2?
$860.95
3)
What is the GPM payment in year 4?
$926.65
4)
What is the change in loan balance in year 4?
($96.80)
5)
What is the beginning balance on the loan at the start of year 5?
$122,425.03