Krzys’ Ostaszewski, http://math.illinoisstate.edu/krzysio/krzys.html
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary
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Spring 2000 Course 2 Examination, Problem No. 47, also Dr. Ostaszewski’s online
exercise No. 198 posted February 28, 2009
Jim began saving money for his retirement by making monthly deposits of 200 into a
fund earning 6% compounded monthly. The first deposit occurred on January 1, 1985.
Jim became unemployed and missed making deposits 60 through 72. He then continued
making monthly deposits of 200. How much did Jim accumulate in his fund on
December 31, 1999?
A. 53572
B. 53715
C. 53840
D. 53966
E. 54184
Solution.
Since the deposits are made monthly, it will be best to count time in months. In order to
do that, we also note that the effective monthly interest rate is 0.50%. Jim made 59
deposits of 200 at times 0, 1, 2, …, 58, and then additional 108 deposits of 200 at times
72, 73, …, 179. The accumulated value at time 180 is:
200 ⋅ s59 0.50% ⋅1.005121 + 200 ⋅ s108 0.50% = 53839.83.
Answer C.
© Copyright 2009 by Krzysztof Ostaszewski.
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