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

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Unformatted text preview: 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 Todays 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...
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This note was uploaded on 11/02/2011 for the course ACTSC 371 taught by Professor Wood during the Fall '08 term at Waterloo.

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

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