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Perpetuities

# Perpetuities - How much did the donor originally contribute...

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Perpetuities Like annuities, perpetuities have the same cash flows all occurring at equal intervals, but they continue forever with no maturity date (they are perpetual ). With annuities, the payments ( C ) exceed the interest income (interest expense, in the case of a loan). 1

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Perpetuities Before we said the PVA is: The formula for a perpetuity is: 2 + = r) (1 1 - 1 r C PVA t r C PV perp = PMT PV r =
Perpetuity Example A charity receives never ending annual income of \$150,000 from a trust fund established by a generous donor several years ago. The trust fund earns a fixed annual return of 5%. How much did the donor originally contribute to establish this fund? 3

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Perpetuity Example 4 A charity receives never ending annual income of \$150,000 from a trust fund established by a generous donor several years ago. The trust fund earns a fixed annual return of 5%.
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Unformatted text preview: How much did the donor originally contribute to establish this fund? 000 , 000 , 3 \$ .05 \$150,000 r C PV perp = = = Perpetuity Example • The investment is generating income equal to that of the payment ( C ), so the 5 r = 0.05 Year Beginning Payment Interest Principal Ending 1 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 2 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 3 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 4 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 5 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 6 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 7 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00 8 \$3,000,000.00 \$150,000.00 \$150,000.00 \$0.00 \$3,000,000.00...
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