Tutorial03_-_soln

# Tutorial03_-_soln - Problem Set 3: ACTSC 231 Mathematics of...

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Unformatted text preview: Problem Set 3: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. (a) Noticing formulae s n e i = (1 + i ) n- 1 i and a n e i = 1- v n i , we immediately have i + 1 s n e i = i + i (1 + i ) n- 1 = i [(1 + i ) n- 1] + i (1 + i ) n- 1 = i (1 + i ) n (1 + i ) n- 1 = 1 (1+ i ) n- 1 i (1+ i ) n = 1 1- v n i = 1 a n e i . (b) Consider two ways to repay a loan of \$1 in n years. One way is to repay level annual payments for n years at the end of each year. The level payment, say X , should satisfy the equation X a n e i = 1. In other words, the annual level payment is 1 a n e i . In the other way, at the end of each year, the borrower pays the interest due, which is \$ i , and deposit \$ Y into a savings account so that the savings account will accumulate to exactly \$1 at the end of n years. This \$1 will be used to payoff the loan amount. Therefore, the annual deposit Y is determined by Y s n e i = 1, i.e., the annual deposit Y = 1 s n e i . In these two ways, it costs the borrower either \$ i + 1 s n e i or 1 a n e i at the end of each year for the same n years to repay the same loan of \$1. Thus, the annual total repayment must be equal, i.e.,loan of \$1....
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## This note was uploaded on 07/13/2011 for the course ACTSC 231 taught by Professor Chisholm during the Winter '09 term at Waterloo.

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Tutorial03_-_soln - Problem Set 3: ACTSC 231 Mathematics of...

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