The Mathematics of Money

190 Chapter 4 Annuities

9. Phyllis took out a 6-year loan to buy a new car. She borrowed $18,000 and the interest rate was 7.56%. Assuming
   she makes all payments as scheduled, how much will she owe after 3 years, when she is halfway through the term of
   the loan?

C. Consolidation and Refi nancing

10. Luke and Stacey have 21 years remaining on their mortgage, for which the interest rate is 8½% and the monthly
    payment is $915.72. They have made all of their payments as scheduled. Mortgage rates have recently come down
    quite a bit, and they are thinking about refi nancing.
    a. How much do they owe today?
    b. If the refi nance their loan by replacing it with a new, 21-year loan at 5.5%, what will their new payment be?
    c. How much would they save by doing this?
    d. Suppose that instead of a 21-year loan, Luke and Stacey decided instead to take out a new, 30-year loan at 6.5%.
    In that case, what would their new payment be, and how much would they save?


11. Kalpana has accumulated the following collection of loans:

Loan Type

Monthly

Payment

Remaining

Payments Interest Rate

Mortgage $875.19 24 years 7.5%

Car loan $335.99 38 payments 8.95%

Personal loan $101.49 45 payments 12.55%

Motorcycle loan $202.15 17 payments 9.75%

To tal $1,514.82

a. She is planning on refi nancing her mortgage. Suppose she refi nances her mortgage with a new 24-year loan at a

6.3% interest rate. What would her new mortgage payment be? How much would she save by doing this?

b. How much in total does she owe now for all of her loans?

c. Instead of just borrowing enough with her new mortgage to pay off her old one, her mortgage broker has told her

that she could borrow enough to pay off all of her loans with the new mortgage. If she does this, what would her

new mortgage payment be?

d. Your answer to (c) should be quite a bit lower than the total of her current monthly payments. The interest rate on

the new mortgage is lower than the current rates on each of these loans. Does this necessarily mean that she will

save money by consolidating all of these loans into her new mortgage?

D. Grab Bag

12. Ian took out an $80,000 business loan. His payments are quarterly, the interest rate is 9.75%, and the term of the loan
    is 8 years. He has made all of his payments exactly as scheduled, and now has 5 years remaining on the loan.
    a. Construct an amortization table for the fi rst 3 quarters of his loan.

Month Payment Interest Principal

Remaining

Balance

1

2

3