Homework 3, Spring 08 answer
(Total 20 points)
Due on Feb. 11, Tue.
Q1
: (3
×
2): (a) When the interest rate is 5%, what is the present value of an as
set that gives you $140 this period and $420 next period?
(b) When the interest rate is 4%, what is the present value of an asset that perpetu
ally gives you $300 every period?
Answer
: (a) It is 140 +
420
1
.
05
= 140 + 400 = 540.
(b) Recall that
ω
∑
∞
t
=1
(
1
1+
r
)
t

1
=
ω
1
1

1
1+
r
=
ω
(1+
r
)
r
. Hence it is
300
·
1
.
04
0
.
04
= 7800.
— One may use the approximate formula
ω
r
, which delivers
300
0
.
04
= 7500.
Q2
: (4): Consider the twoperiod consumption/saving problem. Marina’s prefer
ence over consumption streams is represented by
u
(
x
1
,x
2
) = ln
x
1
+ 0
.
9ln
x
2
. When
her earning stream is (37
,
21) and the interest rate is 5%, how much is her saving in
the ﬁrst period? —
Perform the solution process
.
Answer
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 Spring '10
 d
 Interest, Certainty Equivalent, Harshad number, Tier One, Oskar

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