1. Consider a constant payment mortgage of $100,000, maturity 30 years, interest rate 6%, monthly payments.

(a) What is the monthly payment?
(b) What is the principal payment and interest payment in the second month?
(c) What is the outstanding balance after 5 years?

2. Consider a constant amortization mortgage of $100,000, maturity 30 years, interest rate 6%, monthly payments.
(a) What is the first month's payment?
(b) What is the principal payment and interest payment in the second month?
(c) What is the outstanding balance after 5 years?

3. Consider an interest only mortgage of $100,000, maturity 30 years, interest rate 6%, monthly payments.
(a) What is the monthly payment?
(b) What is the principal payment and interest payment in the second month?
(c) What is the outstanding balance after 5 years?

4. Consider an adjustable rate mortgage of $100,000, no payment cap, no interest rate cap,
2% margin, annual adjustment, annual payments, 3 year maturity, initial index rate:
7%
(a) What is the first year's payment?
(b) If the second year index rate is 9%, and the third year index rate is 13%, what
is the second year and third year's payments?
(c) If the index rates are the same as (b), if there is an annual interest rate cap of
3%, what is second year and third year's payment?

5. Consider a constant payment mortgage of $100,000, maturity 30 years, interest rate 6%, monthly payments. What is the yield of the mortgage if
(a) No point, no prepayment.
(b) No point, prepaid after 10 years?
(c) 1 point and no prepayment
(d) 1 point, prepaid after 10 years, no prepayment penalty
(e) 1 point, prepaid after 10 years, 2% of prepayment penalty

6. Consider a constant payment mortgage of $100,000, maturity 30 years, interest rate
6%, monthly payments with 2 up front points. What is the value of the value of the mortgage after 4 years, if the market yield after 4 years is
(a) 6%
(b) 5%
(c) 7%

7. Suppose you are considering taking out a constant payment mortgage of $100,000, maturity 30 years, monthly payments. The bank offers a mortgage table with the following options:
(1). No point, 7% mortgage interest rate;
(2). 1 point, 6.5% mortgage interest rate;
(3). 2 points, 6% mortgage interest rate.

Which one of the above would you choose if
(a) You will held the mortgage until maturity
(b) You will prepay the mortgage after 5 years
(c) You will prepay the mortgage after 10 years

8. Consider an adjustable rate mortgage of $100,000, no payment cap, no interest rate cap,
2% margin, annual adjustment, annual payments, 3 year maturity, initial index rate:
7%. Suppose we project that the second year index rate is 8.5%, the third year index rate is 10%. What is the APR of this ARM based on the forecasted interest rate?

9. Suppose you took out a mortgage with $100,000, 6% interest rate, 30 year amortizing and 10 year maturity balloon mortgage 5 years ago. Initially there were 2 up front points on this mortgage. Now suppose that you can refinance the existing mortgage loan with a new loan of 5 years, with 1 up front point and interest rate 5%. If the transactions cost is $5,000, do you want to refinance now? (Assuming no prepayment option value)

10. Consider a three year interest only mortgage of $1,000,000, the interest rate is 10%. Suppose the hazard rates and conditional loss rates are as follows:
Year Hazard Rate Conditional Loss Rate
1 2% 20%
2 3% 35%
3 3% 40%

a. What are the unconditional default probabilities of year 1, 2 and 3 defaults?
b. What is the yield degradation of year 2 default?
c. What is the expected rate of return on this mortgage?