As the examples of this section hopefully demonstrate, a change in the payment stream
need not stop us from calculating an account’s future value. Such changes do, however,
require us to break the problem into parts. The chronological approach that we have used in
this section is an effective way of doing this in many cases. In Section 4.7, we will see an
alternative way of looking at things that may prove more useful in other situations.EXERCISES 4.6
A. “Annuities” Whose Payments Stop- a. Suppose that you invest $350 a quarter for 10 years at 8%. How much will you have at the end of the 10 years?
b. Suppose that you then stop making payments, but keep the account open and your money continues to earn 8%
compounded quarterly for the next 25 years. How much will your account grow to? - Destiny has been depositing $3,000 each year into an account earning 9.25% for the last 15 years. She has 20 years to
go until retirement.
a. How much does she have in her account today?
b. Assuming she decides to stop making new deposits but keeps her account open, earning the same rate, how much
will she have when she retires in 20 years?
c. Assuming she decides to keep making $3,000 annual deposits, and her account continues to earn 9.25%, how
much will she have when she retires in 20 years? - If you deposit $100 each month into an account earning 7% for 20 years, and then stop making deposits but keep your
money invested, earning this same rate for another 10 years, how much in total will you have in the end? - Based on the scenario in Exercise 3, how much total interest would you earn?
- When he was 3 years old, Toby’s parents started investing $25 each week in an investment account for him, thinking he
would use the money for college. When he was 18, his parents stopped making these deposits, but Toby didn’t need to
money for college since he won a football scholarship. He kept the money invested, but didn’t put any more money in
the account.
Assuming that his account earns 7.8%, how much will he have in it when he turns 65? How much of that total will be
from interest? - I deposited $25 each week into a savings account earning 5% for 1 year. Then I stopped making deposits and just let
the account grow at compound interest for the next 3 years. How much total interest did I earn?
B. “Sinking Funds” Whose Payments Stop- I want to have $200,000 in an investment account 20 years from now and plan to reach this goal by making equal
quarterly deposits for the next 12 years, and then stopping the deposits and just letting the account grow. My account
earns 10%. How much do I need to have in the account when I stop making deposits? How much should each of my
quarterly deposits be?
Copyright © 2008, The McGraw-Hill Companies, Inc.
Exercises 4.6 195