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E120
Homework 1 Solutions
1. (a) Compounded 5 times: 2000
·
(1 + 0
.
05)
5
(b) 2000
·
(1 + 0
.
05)
10
(c) 2000
·
(1 + 0
.
10)
5
(d) Due to compounding.
2. I assume the interest rates given are being compounded annually.
(a)
10000
(1+0
.
04)
12
(b)
10000
(1+0
.
08)
20
(c)
10000
(1+0
.
02)
6
3. Assuming interest rate is being compounded annually, we should compare $5000 to
$10000
(1+0
.
07)
10
.
4. I assume interest rate is being compounded annually.
(a) 3996
·
(1 + 0
.
08)
7
(b) 3996
·
(1 + 0
.
08)
47
(c)
x
·
(1 + 0
.
08)
18
= 3996, solve for
x
.
5. First form of payment:
PV
1
=
1000
1
.
05
+
1000
1
.
05
2
+
1000
1
.
05
3
= 2723
.
25.
Second form of payment:
PV
2
=
x
1
.
05
3
, where
x
is payment at the end of the third year.
Being indiﬀerent between the two forms implies
x
1
.
05
3
= 2723
.
25, so that
x
= 3152
.
50.
6. Present value of revenue for investment:
4000
1
.
02
+
4000
1
.
02
2
+
4000
1
.
02
3
= 11535
.
53.
Present value of cost for investment:
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 Summer '11
 ALDER

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