# 332mid09 - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Oct. 16, 2009 Fang/Kan RSM332 MID-TERM EXAMINATION Pomorski/Yang DURATION - 2 hours Aid Allowed: Silent electronic calculator and one 1-sided 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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1. (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 semi-annual 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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332mid09 - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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