Mortgage Calculations and Decisions
Study Questions
1. Calculate the original loan size of a fixed-payment mortgage if the monthly payment is $1,146.78, the annual interest is 8.0%, and the original loan term is 15 years.
2. For a loan of $100,000, at 7 percent interest for 30 years, find the balance at the end of 4 years and 15 years.
3. On an adjustable rate mortgage, do borrowers always prefer smaller (tighter) rate caps that limit the amount the contract interest rate can increase in any given year or over the life of the loan?
4. Consider a $75,000 mortgage loan with an annual interest rate of 8%. The loan term is 7 years, but monthly payments will be based on a 30-year amortization schedule. What is the monthly payment? What will be the balloon payment at the end of the loan term?
5. A mortgage banker is originating a level-payment mortgage with the following terms:
Annual interest rate: 9 percent
Loan term: 15 years
Payment frequency: monthly
Loan amount: $160,000
Total up-front financing costs (including discount points): $4,000
Discount points to lender: $2,000
a. Calculate the annual percentage rate (APR) for Truth-in-Lending purposes.
b. Calculate the lender's yield with no prepayment.
c. Calculate the lender's yield with prepayment is five years.
d. Calculate the effective borrowing costs with prepayment in five years.
N = 60 I = ? PV = -$158,000 PMT =$1,622.83 FV =$128,108.67
6. Give some examples of up-front financing costs associated with residential mortgages. What rule can one apply to determine if a settlement (closing) cost should be included in the calculation of the effective borrowing costs?
7. A homeowner is attempting to decide between a 15-year mortgage loan at 5.5 percent and a 30-year loan at 5.90 percent. What would you advise? What would you advise if the borrower also has a large amount of credit card debt outstanding at a rate of 15 percent?
8. Suppose a one-year ARM loan has a margin of 2.75, an initial index of 3.00 percent, a teaser rate for the first year of 4.00 percent, and a cap of 1.00 percent. If the index rate is 3.00 percent at the end of the first year, what will be the interest rate on the loan in year two? If there is more than one possible answer, what does the outcome depend on?
9. Assume the following for a one-year rate adjustable rate mortgage loan that is tied to the one-year Treasury rate:
Loan amount: $150,000
Annual rate cap: 2%
Life-of-loan cap: 5%
Margin : 2.75%
First-year contract rate: 5.50%
One-year Treasury rate at end of year 1: 5.25%
One-year Treasury rate at end of year 2: 5.50%
Loan term in years: 30
Given these assumptions, calculate the following:
a. Initial monthly payment
b. Loan balance end of year 1
c. Year 2 contract rate
d. Year 2 monthly payment
e. Loan balance end of year 2
f. Year 3 contract rate
g. Year 3 payment
10. Assume the following:
Loan Amount: $100,000
Interest rate: 10 percent annually
Term: 15 years, monthly payments
a. What is the monthly payment?
b. What will be the loan balance at the end of nine years?
c. What is the effective borrowing cost on the loan if the lender charges 3 points at origination and the loan goes to maturity?
d. What is the effective borrowing cost on the loan if the lender charges 3 points at origination and the loan is prepaid at the end of year 9?