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I am not quite sure that this is the correct solution, but here are my
thoughts:
1. Mary has a regular annuity => X = 1000*S5 = 1000 *
((1+0.09)^5-1)/0.09 =
= 5984.71
2. John's case is more interesting. At the year 1 he invests 1000*0.1
dollars at the rate of 8% for 4 years, at the year 2 he invests
2000*0.1 at the rate of interest of 8% for 3 years, and so on.
Therefore Y = 5000 + 100*1.08^4 + 200*1.08^3 + 300*1.08^2 + 400*1.08^1
+ 500 = 6669.91
3. Y - X = 685.20
----------
From: Carolyn J. McElroy
Sent: Tuesday, July 21, 1998 4:27 PM
To: studygroup4a@lists.casact.org
Subject: Uncle!!! - 4A interest theory question from chapter 3
Here's a problem from the chapter 3 material. The correct answer is
supposed to be 685. If someone solves this problem correctly, please
let me know . This is a SOA interest theory problem, and so is
probably more challenging than what we'll see in the exam.
Mary invest 1000 at the end of each year for 5 years at an annual
effective rate of 9% and reinvests the interest at an annual effective
rate of 9%. At the end of 5 years, her investment has value of X.
John invests 1000 at the beginning of each year for 5 years at an
annual effective rate of 10% and reinvests the interest at an annual
effective rate of 8%. At the end of 5 years, his investment has a
value of Y.
Calculate Y - X.
a) 99 b) 147 c) 327 d) 570 e) 685
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