Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 115, 7/28/7
Author of a study manual for exam FM available at:
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary
If you find these exercises valuable, please consider buying the manual or attending the
seminar, and if you can’t, please consider making a donation to the Actuarial Program
at Illinois State University: https://www.math.ilstu.edu/actuary/giving/
Donations will be used for scholarships for actuarial students. Donations are taxdeductible to the extent allowed by law.
Questions about these exercises? E-mail: [email protected]
May 2003 Course 2 SOA/CAS Examination, Problem No. 12, also Study Note FM09-05, Problem No. 3
Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of
i, compounded semiannually. Mike deposits 2X into a different savings account at time
0, which pays simple interest at an annual rate of i. Eric and Mike earn the same amount
of interest during the last 6 months of the 8-th year. Calculate i.
A. 9.06%
B. 9.26%
C. 9.46%
D. 9.66%
E. 9.86%
Solution.
After seven and a half years Eric will accumulate
2'7.5
15
i$
i$
!
!
X #1 + &
= X #1 + &
"
"
2%
2%
and therefore Eric’s interest in the last 6 months of the 8-th year is:
15
i$ i
!
X #1 + & ' .
"
2% 2
i
Mike’s interest in the last 6 months of the 8-th year is 2X ! . By equating the two
2
interest amounts we get
15
i$ i
i
!
X # 1 + & ' = 2X ' ,
"
2% 2
2
i$
!
so that # 1 + &
"
2%
Answer C.
15
= 2, and i ! 9.46%.
© Copyright 2006-2007 by Krzysztof Ostaszewski.
All rights reserved. Reproduction in whole or in part without express written
permission from the author is strictly prohibited.
Exercises from the past actuarial examinations are copyrighted by the Society of
Actuaries and/or Casualty Actuarial Society and are used here with permission.