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Q
uantitative
R
easoning &
P
roblem
S
olving
370
© 2014 Pacific Crest
M
odel
2: I
dentical
T
wins
, D
ifferent
S
trategies
YOUR
TURN!
Scenario:
Sheri and Terri are twins who began to work at age 20 with identical jobs and
identical salaries. At the beginning of each year starting at the age of 30, they
received identical bonuses of $2500.
In other ways the twins were not identical. Early in life Sheri was conservative.
Each year she invested the $2500 bonus in a savings program earning 8%
interest compounded quarterly. At age 40, Sheri decided to have some fun and
began spending her $2500 bonus each year, but she let her earlier investment
continue to earn interest. This continued until she was 65.
In contrast, for the first 10 years she worked, Terri spent her $2500 bonuses.
At age 40, she began to invest her bonus every year in the same kind of
account (8% interest compounded quarterly). This continued until Terri was
65 years old.
a. How much, in total, did each woman deposit into her account?
b. Which sister deposited more money? How much more?
c. Which sister had more money in her account at 65? How much more?
d. What are two advantages of Sheri’s savings plan?
e. What are two advantages of Terri’s savings plan?
f. A moral to the story of Sheri and Terri exists. What is the moral? What can you learn from their
story?
g. While they were saving and/or spending, assume that there was a 2.5% inflation rate each year.
What is the present value of each woman’s account, considering this inflation?
At age 65 both women turn their accounts (still earning 8%) into annuities to be paid out quarterly over
a 30 year period.
h. Ignoring the effects of inflation, how much money will each receive every quarter over that time?
i. What is the total payout that each will receive from their annuities, assuming that they both live
to age 95?
C
ritical Thinking Questions
Developing your understanding
1. For an investment, which is larger, the present value or the future value? Why?