Question

1. Your local lender offers you a fixed-rate mortgage with the following terms: $220,000 at 4.75% for 30 years, monthly payments. The lender will charge you two discount points and the loan has a 3% prepayment penalty.

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

   B. (1 pt) How many points are required to yield an APR of 5.25%?
   Answer: _______

2. Suppose you take a fixed-rate mortgage for $200,000 at 5.00% for 30 years, monthly payments.

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

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

3. Suppose you take a $175,000 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.

A. (1 pt) How many monthly payments are remaining after the extra lump sum

payment is made?

Answer: ________

B. (1 pt) What is your net interest savings over the life of the loan, assuming the

loan is held to its maturity?

Answer: ________

4. You just took a fixed-rate mortgage for $250,000 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.

A. (1 pt) What is your net interest savings over the life of the loan, assuming the

loan is held to its maturity?

Answer: ________

B. (1 pt) If you make this higher payment and hold the loan for its full life, what

is the effective cost of the loan?

Answer: ________

5. Suppose you have two options on a $150,000, 30-year, fixed-rate mortgage. Option one is a 5.25% contract rate with 2.00 points. Option two is 5.00% contract rate but you have forgotten how many discount points are charged. Both loans have a 3% prepayment penalty for the first eight years of life.

A. (1 pt) Calculate the number of points on option two that would equalize the

APRs of the two loans.

Answer: ________

B. (1 pt) Calculate the number of points on option two that would equalize the effective costs of the two loans over a five-year holding period.

Answer: ________

Answer 1

Question 1:

A.2 points = 2% which when divided over 30 years makes it = 0.067% per year.

So, APR of the loan = 4.75 +0.067 = 4.8167%.

We do not take into consideration the prepayment penalty.

APR of the loan = 4.82% (Rounded to 2 decimals).

B. For the APR to 5.25%, the points to be considered are as follows

Total APR = Loan rate + annual point

5.25 = 4.75 + point/30

0.50 = points/30

Number of points = 30*0.15 = 15 points

How many points are required to yield an APR of 5.25%? (Answer 15 points)

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