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19. An annuitt pays 12 at time 0, 17 at time 4, 22 at time 8, and so on forever. Determine the present value of the payments
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Answer #1

This series can be broken down into two:
Series 1: Constant payments of 17
Series 2: Arithemtic Gradient of 5
and Cash flow of -5 at time 0

Present Value=-5+17/r+5/r^2

Given,
1/(1+EAR)^4=0.80

rate compounded once in four years r=(1+EAR)^4-1=1/0.80-1=25.00%

Present Value=-5+17/(1+r)+5/r^2=-5+17/(25%)+5/(25%)^2=143

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