Q:
For \$800,000 invested today, an insurance company promises to start making perpetual payments to you beginning seven years from now. What must these perpetual payments be if the long-term savings rate is expected to remain constant at 5.5%?
A) \$60,669
B) \$64,006
C) \$166,249
D) Present value is infinite because payments continue into infinity.
A:
We must first link the \$800,000 today to the period when the perpetuity payments will begin. In this case: PV=800,000; I=5.5; N=6; thus, FV=1,103,074. Note that the \$1,103,074 is the value of the perpetuity by the end of the sixth year. We also know that:
Present Value of a Perpetuity @ period t = [cash flow for period t+1]
[Period interest rate]
Therefore:
Present value of \$1,103,074 @ period 6 = [Cash flow beginning period 7]
0.055
Therefore, the cash flow beginning in period 7 and continuing indefinitely is (\$1,103,074)*(0.055) = \$60,669.08.

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