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# A2_sol - ActSc 371 Assignment#2 Solutions Question 1 As...

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ActSc 371: Assignment #2 Solutions Question 1 As calculated in class, the present value of the rental payments is 75 1 . 04 + . . . + 75 (1 . 04) 20 = 75 . 04 1 - (1 . 04) - 20 = 1019 . 27 Today’s actions provide us with a cash inflow of this amount and a cash outflow of \$1000 (the amount spent on the machine). Therefore the net cash flow to us today is \$19.27. The deposit is equal to the difference between the rental payment of \$75 and the interest payment. The interest payment is 4% of the principal, which is equal to (using the middle expression above) 75 1 - (1 . 04) - 20 . Therefore the amount of each deposit is 75(1 . 04) - 20 . It is also acceptable to say that the deposit is equal to 75-(.04)(1019.27)=75-40.77=34.23 The first deposit sits in the account for 19 years, the second for 18 years . . . the nineteenth for one year. Therefore the account balance with Bank B in twenty years will be B = 75(1 . 04) - 20 (1 . 04) 19 + 75(1 . 04) - 20 (1 . 04) 18 + . . . + 75(1 . 04) - 20 (1 . 04) = 75 1 1 . 04 + 1 (1 . 04) 2 + . . . + 1 (1 . 04) 19 Alternatively, the balance will be B = 34 . 23(1 . 04) 19 + 34 . 23(1 . 04) 18 + . . . + 34 . 23(1 . 04) = 34 . 23(1 . 04) 19 " 1 + 1 1 . 04 + . . . + 1 1 . 04 18 # = 34 . 23(1 . 04) 19 1 - (1 . 04) - 19 1 - (1 . 04) - 1 = 985 . 07 The cash inflow in twenty years will be B + 75 = 75 1 + 1 1 . 04 + 1 (1 . 04) 2 + . . . + 1 (1 . 04) 19 = 75 1 - (1 . 04) - 20 [1 - (1 . 04) - 1 ] = 75(1 . 04) . 04

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A2_sol - ActSc 371 Assignment#2 Solutions Question 1 As...

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