180 Chapter 4 Annuities
- A company knows that it will need to pay $750,000 each year for the next 10 years to clean up toxic pollution at a
former plant site. Management wants to set aside a lump sum now that will be enough to provide for those costs. If the
money earns 5% interest how much would the company need to set aside today? - Jack won a sweepstakes jackpot, payable in the form of a 15-year annuity with equal annual payments beginning
immediately and totaling $3,000,000. If he wishes, he can choose to instead receive the present value of this annuity,
calculated by using a 7^1 / 2 % interest rate. How much would he get under that option? - As the result of a personal injury lawsuit, Garret won a $1,800,000 judgment. However, he does not get the money
all at once; the judgment will be paid to him in 20 equal annual installments totaling $1,800,000, starting right away.
Garret doesn’t want to wait for his money, though. A company offers to give him a lump sum immediately, in exchange
for all of his payments from the judgment. If the interest rate is 8%, how much would this lump sum be?
F. Grab Bag
- Find the present value of a 10-year ordinary annuity with $500 quarterly payments if the interest rate is 5%.
- Miguel and Cindi borrowed $189,750 to buy their house, for which they took out a 30-year loan at 7.29%. (a) Find their
monthly payment. (b) What would their payment have been if they had instead taken out a 15-year loan at the same
interest rate? - If Emilio (from Exercise 20) does continue to only pay $50 a month, how much total interest will he pay before his
credit card account is paid off? - Find the present value annuity factor for an 8-year annuity with semiannual payments and an interest rate of 4.49%.
- A letter to the editor of the local newspaper complains that $775,000 “wasted” on a “useless” economic development
study could have been better used. The writer claims that “if the money had been invested at just 4% interest, it could
have provided enough money to keep an additional cop on the streets for the next 20 years!” Assuming a level cost per
year over the next 20 years, what is the writer assuming it costs to pay a police offi cer for a year? - Jamie has just been accepted to pharmacy school. When she met with a college fi nancial aid offi cer, he told her that,
at the current 4.35% interest rate, she could expect that after graduating her student loan payments would be about
$275 a month for 20 years. According to these fi gures, how much student loan debt will she have when she graduates? - Find the monthly payment on a 4-year, $11,500 loan at 11.97%.
- Claudette owes $3,725.86 on her credit card. She has stopped using the card, and wants to get herself out from under this
debt in 1 year. How much will she need to pay each month to do this, assuming the card carries a 15.99% interest rate?
G. Additional Exercises
- Kathy’s monthly payment on her 30-year mortgage is $725.14. Her interest rate is 6.59%.
a. How much total interest would Kathy have saved if, instead of her 30-year loan, she had gone with a 15-year loan
at the same interest rate?