ISyE 3025
Engineering Economy
Spring 2011
Professor Nagi Gebraeel
Solution to Exam 1B
1. An individual contributes $200 per month to a “401(k)” retirement account. The account earns interest
at a nominal interest rate of 8% compounded monthly (i.e. interest is credited monthly). What is the
value of the account after 35 years?
(a) $310
,
000
(b) $368
,
000
(c) $414
,
000
(d) $447
,
000
(e) $459
,
000
X
Solution:
This cash flow stream can be modeled as an annuity over 35
×
12 months with an interest
rate of 8%
/
12 and a payment of $200 per period.
The future value of this stream is calculated as
follows:
F
=
A
[(1 +
i
)
N

1]
i
=
200[(1 +
.
08
/
12)
35
×
12

1]
.
08
/
12
= $458
,
776
.
2. Money invested at annual nominal interest rate of 6% compounded monthly will triple in approximately
how many months?
12. One way to think about this problem is to hypotheti
cally make a deposit of $1 at time 0 and let it grow for
N
months until it reaches a future value of $3.
Use the equation for
F/P
and solve for
N
as follows:
F
=
P
(1 +
i
)
N
3 = 1
×
(1 +
.
06
/
12)
N
ln 3 =
N
ln(1 +
.
06
/
12)
N
= 220
.
27
.
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 Spring '09
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 Time Value Of Money, Deposit account, bank account, cash flow stream

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