U
NIVERSITY OF
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AROLINA
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ILL
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-F
LAGLER
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USINESS
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CHOOL
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USI
408:
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ORPORATE
F
INANCE
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OLUTIONS TO
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RACTICE
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ROBLEM SET
#1:
T
IME
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ALUE OF
M
ONEY
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A
RZU
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ZOGUZ
1.
Bob and Jane Loveboat are saving to buy a boat at the end of 5 years.
If the boat
costs $25,000, and they can earn 8 percent a year on their savings, how much do
they need to put aside at the end of every year 1 through 5?
You need to find the amount they need to set aside every year such that the
annual savings, invested at 8 percent a year, accumulate to $25,000.
That is,
you have an annuity of $C with FV = $25,000.
Recall that the formula for
the future value of an annuity is given by:
( )
[ ]
r
r
C
FV
t
1
1
−
+
×
=
where C is the annual payment, r is the annual year interest rate, FV is the
future value of the annuity.
Therefore we have:
( )
08
.
1
08
.
1
000
,
25
5
−
×
=
C
.
Solving for C gives, C = $4,261.41
2.
Leeds Autos has just announced its new promotional deal on the new $45,000 Z4
Roadster.
You pay $5,000 down, and then $1000 for the next 40 months.
Its next
door competitor, Chatham Hill Autos will give you a $3000 off the list price
straight away.
If the interest rate is 6% a year, which company is giving a better
deal?
You need to compare the present value of the two streams of payments,
paying $42,000 today, vs. paying $5000 today, plus $1000 for the next 40
months.
Note that the payments are monthly, so we need to use the monthly
rate of 6%/12 = 0.5%.
The present value of Leeds Autos offer:
$5000 + PV(annuity($1000,T=40,r=0.5%))
=
=
()
23
.
172
,
41
$
005
.
1
1
1
005
.
0
1000