Question

A perpetuity has payments of 1, 2, 1, 3, 1, 4, 1, 5, ..... Payments are made at the end of each year. You may assume an annual effective interest rate of 5%. Determine the present value of the perpetuity.

Please give a detailed calculation process, instead of table.

Thank you.

Answer #1

solution:

PV of the payments of 1 at time 1,3,5,... is

= v+(v3)+(v5)+...

= v/(1-(v^2))

= 9.76

PV of payments of 2,3,4,...,at time 2,4,6,... candetermined by
increasing annuity at effective rate

j=1.052 for a 2-year period.

So the PV of the increasing payments is

=(2/j)+(1/(j2)) = 19.51 + 95.18

= 114.69

PV of the total perpetuity = 114.69 + 9.76

= 124.45

Here the PV given (114.69) is as of t=1, not t=0.

so the solution is

=9.76 + (19.51 + 95.18)(1.05^-1)

= **118.94**

ThankYou.....

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