The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

b. Determine how much he owes on this loan now.

c. Construct an amortization table for his next 3 monthly payments.

Month Payment Interest Principal

Remaining

Balance

13

14

15

d. How much total interest will Ian have paid over the entire life of the loan, assuming that he continues to make all

of his payments as scheduled.

e. Between today and the end of the loan’s term, how much total interest will Ian pay, again assuming he makes all

of his payments as scheduled.

f. How much total interest has Ian paid over the course of the fi rst 3 years?

13. I have a student loan with 12 years left to go. My monthly payment is $188.75 and the interest rate is 8.5%. I have the
    opportunity to refi nance this loan with a new 12-year loan at 5%. What will my new payment be? How much will I save
    by refi nancing?


14. Complete the missing entries in the following (partial) amortization table. The interest rate is 7% and the initial balance
    was $207,913. Payments are monthly.

Payment

Number

Payment

Amount

Interest

Amount

Principal

Amount

Remaining

Balance

1 $3,750.00

2 $3,750.00

3 $3,750.00

15. To fi nance a new offi ce building, Hydrotech Nanowidget Inc. borrowed $1,850,000 at 7.45% interest. The company is
    scheduled to make quarterly payments of $59,735 on this loan. Find the amount of the fi rst payment that goes toward
    interest, the amount that goes toward principal, and the remaining balance on this loan after the company makes the
    fi rst payment.

E. Additional Exercises

16. Jenny and Hamid took out a mortgage loan for $122,305 for 30 years at 6.39%. Assuming they make all their
    payments as scheduled, how much total interest will they pay in the fi rst 5 years of the loan?


17. When she retired 5 years ago, Neryssa had $793,000 in her retirement account. She invested the money with an
    insurance company, which agreed to send her monthly payments for 30 years, using her $793,000 as the present value
    of the payments and an interest rate of 5.3%. Every month the company credits her account with the interest due, and
    then withdraws the amount of her monthly payment and sends it to her. What is the balance of her account today?

Exercises 4.5 191