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332mid09a - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Oct. 16, 2009 Fang/Kan RSM332 MID-TERM EXAMINATION Pomorski/Yang SOLUTIONS 1. (a) The effective 6 month interest rate is r * = exp(0 . 05 / 2)- 1 = 0 . 025315. Let x be the amount of your semi-annual withdrawal. The present value of your future withdrawal is PV = x r * 1 (1 + r * ) 19 = 24 . 566 x. Since the present value is equal to 100, we have x = 100 / 24 . 566 = 4 . 07. (b) The future value of Investor A ’s savings at retirement is FV A = 1000(1 . 1) 40 + 1000(1 . 1) 39 + ··· + 1000(1 . 1) = 1000(1 . 1) . 1 [(1 . 1) 40- 1] = 486,852 . (c) Let x be the amount of annual contribution for Investor B . The future value of Investor B ’s savings at retirement is FV B = x (1 . 1) 30 + x (1 . 1) 29 + ··· + x (1 . 1) = x (1 . 1) . 1 [(1 . 1) 30- 1] = 180 . 94 x. In order for FV A = FV B , we need x = 486,852 / 180 . 94 = 2,690.63. (d) The future value of Investor B ’s savings at retirement is FV B = 4500(1 . 1) 40- n + 4500(1 . 1) 39- n + ··· + 4500(1 . 1) = 4500(1 . 1) . 1 [(1 . 1) 40- n- 1] . 1 In order for FV A = FV B , we need 486,852 = 4500(1 . 1) . 1 [(1 . 1) 40- n- 1] ⇒ (1 . 1) 40- n- 1 = 9 . 8354 ⇒ (1 . 1) 40- n = 10 . 8354 ⇒ 40- n = ln(10 . 8354) ln(1 . 1) ⇒ 40- n = 25 ⇒ n = 15 . 2. (a) (i) It is the future value of an annuity of C = 3000, T = 40 and r = 0 . 05: (1 + 0 . 05) 40 × 3000 A 40 . 05 = (1 . 05) 40 × 3000 × 1 . 05 " 1- 1 (1 . 05) 40 # = 362 , 399 . 32 (ii) The value of a T-year growing annuity with C = 40000, g = 0 . 03 and r = 0 . 05 is 40000 . 05- . 03 " 1- 1 . 03 1 . 05 T # ....
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332mid09a - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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