I'm sure that someone else has better logic, but this is how I did it.
1.) We need to get the payments evaluated as of t=6.
[200 s(5) + 1000 (1.07)**5](1.07) = $2731.39
I brought the $200 payments out to time t=5. s(5) is my notation for the
future value of an annuity of 5 years.
1000(1.07)**5 is the future value @ time t=5 of the $1000 initial
payment.
I then multiplied them the two payments at t=5 by 1.07 to bring them to
t=6.
2.) Find the present value of the payments at time t=7, 8, 9
1500a(3) - Q [(a(3)-nv**3)/i]
see page 55 in Parmenter or page 110 in Kellison (2nd ed.)
3.) The future value of the payments at t=6 should equal the present value of
the decreasing annuity evaluated at time t=6.
2731.39 = 3936.47 - Q (2.506)
Q = 480.88
I hope this helps.
Erica
(P.S. - Great Name!)
--------------------------( Forwarded letter 1 follows )---------------------
Date: Thu Sep 24 15:17:01 1998
To: studygroup4a@lists.casact.org
From: szetoe@towers.com
Sender: studygroup4a-return@casact.org
Subject: Spring 1998 exam Question 5
The questions reads:
Leo will make an initial deposit into an account of $1000 at time t=0,
followed by five
annual deposits of $200 at times t = 1, 2, 3, 4, 5. Leo will receive
payments from the
account at times t = 7, 8, 9, starting at $1500 and decreasing by $Q
per year. The
balance in the account after the last payment is $0.
You may assume this account earns an effective annual interest rate of
7%.
Determine Q.
A. Less than $450
B. At least $450, but less than $490
C. At least $490, but less than $530
D. At least $530, but less than $570
E. $570 or more
I keep getting an answer of Q = $621.82 but the answer is B.
Can someone help me please?!?!?
Thanks,
Erica Szeto