Question

the possible answers are 120,140,160,180,200

19. An annuity pays 12 at time 0, 17 at time 4, 22 at time 8, and so on forever. Determine the present value of the payments if the present value of a payment of 1 payable four years from now is 0.80.

Answer 1

Answer is 140

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