1. Fixed-Rate Mortgage Mathematics Problems: (0.25 point each)

1-1, Jack takes a fully amortizing mortgage for $80,000 at 7 percent interest for 20 years, monthly payments. What will be his monthly payment.

1-2, Michelle qualifies to borrow $120,000 on a mortgage at 9 percent for 30 years, monthly payments.

1. What is her monthly payment?
2. How much interest does she pay in the first year of the mortgage?
3. If she decides to repay the mortgage at the end of year, what is the outstanding balance at that time?

1-3, You want to purchase a house that has an asking price of $125,000. You can get a loan for 80 percent of the banks appraised value at 9.5% percent for 30 years, monthly payments. The appraiser values the house at 95 percent of the asking price.

1. What will be your monthly payment if you take the loan?
2. What would be the balance of the mortgage after 5 years?
3. Set up a 5-year amortization schedule showing total annual mortgage payments, total interest, and principal paid annually, and the balance at the end of each year. (Do not set up a monthly amortization schedule to answer this problem.)

1-4, Determine the monthly payment for the following mortgages of $90,000 each.

Mortgage Interest Rate(%) Maturity (in Months) Payment

A 10 360 ??

B 11 300 ??

C 9 300 ??

D 8 260 ??

1-5. How long would it take to pay off the following mortgages? (Never is a possible answer.)

Mortgage Payment ($) Interest Rate(%) Initial Loan ($) Maturity

A 400 10.0 45,000 ??

B 800 10.5 75,000 ??

C 600 11.0 62,000 ??

D 550 11.0 60,000 ??

1. For a 30-year fixed-rate mortgage with balance of $100,000 and mortgage rate of 6.00%, please do solve the followings (0.25 point)
   1. Assuming the borrower will pay the mortgage based on the schedule for next 30 years,
      1. What is the Average Life of the mortgage (in years)?
      2. What is the PV of the mortgage if market mortgage rate goes up to 6.50%?
      3. What is the PV of the mortgage if market mortgage rate goes up to 5.50%?
      4. What is the effective duration according to the formular in slide 53?

1. Assuming the borrower will pay the mortgage based on the schedule for first five years and pay off the mortgage at the end of fifth year,
   1. What is the Average Life of the mortgage (in years)?
   2. What is the PV of the mortgage if market mortgage rate goes up to 6.50%?
   3. What is the PV of the mortgage if market mortgage rate goes up to 5.50%?
   4. What is the effective duration according to the formular in slide 53?

1. (0.25 point, fixed-income concept) Implied Forward Rate question: If you have two options to investment your $10,000: First one is an one-year Certificate of Deposit (CD) with simple annual interest rate of 1%; The second one is a two-year Certificate of Deposit (CD) with simple annual interest rate of 2% for year 1 and year 2. There are two questions:
   1. What is the implied one-year forward one-year CD rate?
   2. Which investment between the two do you prefer? Why?

1. (0.25 point, fixed-income concept) Day count/Compounding question: There are two one-year $10,000 investments, assuming both are default-free investments:
   1. Investment I pays coupon of 6.00%, paying semi-annually with day-count of 30/360;
   2. Investment II pays coupon of 6.10%, paying annually with day-count of Actual/365;

You can purchase each investment at price of 100, or pay $10,000 upfront.

Which investment do you prefer? Why?

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