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ISyE 3025, Spring09 , HW1, Solutions
This homework is intended for Learning Cycle 1, leading to Exam 1
1.
In 1948 your grandfather left your mother a $5,000 U.S. government bond, to be used for your education.
The
annual interest rate was 1.9%.
The annual interest was left to accumulate with the bond according to
compound interest.
Then your mother redeemed (cashed in) the bond. What were the
cash proceeds
many
years later, in 2004?
Solution:
Answer uses
F/P
factor.
F
0
i
per year
N
P
F = $5,000 (F/P, 1.9%, 2004-1948) =
5,000(1 + .019)^56 = $14,346.
2.
You wish to join a club that has an initiation fee of $40,000.
You only have $23,000 available for this right
now.
You can invest in a fund that pays 3.5% per year.
If you invest your money in this fund, how many
years
must you wait until it will grow to the required amount for the initiation fee?
[Assume the initiation fee
does not change, due to inflation or other reasons]
Solution
:
Answer involves manipulation of
F/P
factor.
$40,000 = $23,000 (F/P, 3.5%, N) = 23,000(1 + .035)^N
40,000/23,000 = 1.035^N
N = ln(40/23)/ln(1.035) = 0.5534/0.0344 = 16.09, round up to 17 because interest is paid at the end of the year
on this account.
It will take 17 years to accumulate.
[Can also solve by trial-and-error.]
[Diagram is similar to previous one.]
3.
A certain investment is available that promises to return $7,000 five years from now.
If the investor's "time
value of money" is 4.5% per year, find the
equivalent present value
of this proposed investment.
Solution
:
Answer uses
P/F
factor.
P = $7,000 (P/F, 4.5%, 5) = 7,000(1.045)^(-5) = $5,617.
[Diagram is similar to previous one.]
4.
You expect to receive a future amount at the end of year 200Y.
However, you wish instead to receive this
amount earlier, at the end of year 200X, with years shown in the table.
At the annual interest rate shown in the
table, what is the
equivalent amount
at the end of Year 200X?
Future amount Year 200Y Annual interest rate Year 200X
$ 2,000
2008
6%
2005
Solution
: Answer uses
P/F
factors.
Take year 2005 as reference point.
P = $2,000 (P/F, 6%, 2008-2005) = $2,000(1.06)^-3 = $1,679.
5.
You are presented with two investment opportunities, A and B as described below.
A choice of either one
would require the initial investment now (if you select either investment opportunity, you cannot invest less or
more in that opportunity, only the amount shown).
In addition, you can
always
invest in a fund that pays 5%
per year.
You currently have $4,000 to invest.
If you wish to
maximize your cash amount
at the end of year 6,
which of the two investments, A or B, is the better choice?
You cannot select both.
Explain numerically.
Investment opportunity
A
B
Initial investment needed
$4,000
$3,200
Annual interest rate
7%
9%
Length of investment
6 years
5 years
Solution
:
Answer requires use of
F/P
factor, selection of a
common horizon time
, and
consideration of
unused funds
, which would be invested at 5%.