2.) I got the formula for this out of the 140 Textbook by Kellison.
The accumulated value of this annuity is equal to
The sum of the annuity payments + the accumulated value of interest
It's going to take me a bit to explain the formula, so bear with me. If
you have the Kellison's text (2nd ed.), the formula is on page 138.
This is the formula assuming a payment of $1 at the beginning of each period:
n + i(Is)n:j (Is)n:j is the accumulated value of an increasing
annuity-due for n periods at an interest rate of j%.
j is the reinvestment interst rate
i is the amount of interest the payment receives
The formula for (Is)n is on page 56 in Parmenter or 138 in Kellison (2nd Ed.).
Y = 5(1000) + [(.1)1000(6.336 - 5)]/.08
Y = 5000 + 1670 = 6670
Y - X = 6670 - 5984.71 = 685.29
Hopefully, this makes some sense. If not, I'm sure someone else can put out a
clearer explanation.
------------------( Forwarded letter 1 follows )--------------------
Date: Tue Jul 21 19:50:27 1998
To: studygroup4a@lists.casact.org
From: Carolyn.McElroy@ey.com
Sender: studygroup4a-return@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