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UNIVERSITY OF TORONTO
Joseph L. Rotman School of Management
Oct. 16, 2009
Fang/Kan
RSM332
MIDTERM EXAMINATION
Pomorski/Yang
DURATION  2 hours
Aid Allowed: Silent electronic calculator and one 1sided 8
1
2
”
×
11” crib sheet
Name:
Student Number:
Circle the section that you are registered in:
Kan (Mon)
Kan (Tue. 9a.m.–11a.m.)
Kan (Tue., 1p.m.–3p.m.)
Yang (Mon.)
Yang (Tue.)
Fang
Pomorski (Wed. 2–4p.m.)
Pomorski (Wed. 4p.m.–6p.m.)
Instructions
1. Write all your answers on the examination paper.
2. Answer ﬁve out of six questions. Each question is worth 20 marks. Do not answer all
six questions! In the table below, cross out the question that you choose not to answer.
Question
Marks
1
2
3
4
5
6
Total
1
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View Full Document1. (a) Suppose the interest rate is 5%/year, continuously compounded. You put $100
in your bank account today and plan to withdraw a ﬁxed amount from it every six
months forever, with the ﬁrst withdrawal starting at 10 years from today. What is the
amount of the semiannual withdrawal that you can aﬀord? (6 marks)
(b) Two investors,
A
and
B
, plan to retire after 40 years, but save for their retirement
in very diﬀerent ways. Investor
A
puts $1,000 into his retirement account at the
beginning of each year for 40 years (i.e., at
t
= 0
,
1
,...,
39). Suppose the eﬀective
annual interest rate is 10%/year. How much money does investor
A
have at retirement
(i.e., at
t
= 40)? (4 marks)
(c) Following part (b), investor
B
does not make any contributions for the ﬁrst 10
years, but tries to make it up with higher contributions at the start of each year for
the remaining 30 years, i.e., he will make contributions at
t
= 10
,
11
,...,
39. What is
the annual contribution of investor
B
so that he can have the same amount of money
as investor A when they retire. (4 marks)
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 Spring '10
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