Question

1. Your local lender offers you a fixed-rate mortgage with the following terms: $200,000 at 5.50% for 30 years, monthly payments. The lender will charge you two discount points and the loan has a 4% prepayment penalty.

   A. (1 pt) What is the annual percentage rate (APR) of the loan?

   B. (1 pt) How many points are required to yield an APR of 5.75%?

2. Suppose you take a fixed-rate mortgage for $175,000 at 4.50% for 30 years, monthly payments.

   A. (1 pt) How much of the payment is interest for month 100?

B. (1 pt) How much total interest do you pay in the first six years?

3. Suppose you take a $250,000 thirty-year fixed-rate mortgage at 5.25%, two discount points, monthly payments. At the end of the first year you inherit $20,000 from your now-favorite aunt. You decide to apply this $20,000 to the principal balance of your loan.

   1. (1 pt) How many monthly payments are remaining after the extra lump sum payment is made?

   2. (1 pt) What is your net interest savings over the life of the loan, assuming the loan is held to its maturity?

4. You just took a fixed-rate mortgage for $200,000 at 4.50% for 30 years, monthly payments, two discount points. Before you make any payments you receive a nice raise so you plan to pay an extra $160 per month on top of your normal payment.

   1. (1 pt) How many monthly payments do have to make at the higher payment to fully amortize the loan?

   2. (1 pt) What is your net interest savings over the life of the loan, assuming the loan is held to its maturity?

   3. (1 pt) If you make this higher payment and hold the loan for its full life, what is the effective cost of the loan?

5. Suppose you take a 30 year fixed-rate mortgage for $180,000 at 6.25%, monthly payments with a two discount point rebate (negative discount points) to the borrower. Assume that you have no other financing fees.

A. (1 pt) What is the APR of the loan?

B. (1 pt) What is the effective cost with a five-year holding period?

6. Suppose you borrow $200,000 at 5% for 30 years, monthly payments. You pay 2 discount points.

A. (1 pt) Your APR on this loan is 5.375%. What amount of other financing fees did you pay?

B. (1 pt) Suppose that your effective cost over a five-year holding period is 5.625%. What amount of other fees did you pay?

7. Suppose you borrow $150,000 at 6% for 30 years, monthly payments with two discount points. Your mortgage contract includes a prepayment penalty of 4% over the entire loan term.

A. (1 pt) What is the APR of this loan?

B. (1 pt) What is the effective cost if you prepay the loan at the end of year five?

Please include the calculator solutions (Ex. N=, PMT=, PV=)

Answer 1