Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $ 9 comma 000 in the first year, and will grow by 5 % per year, forever. If the interest rate is 10 %, how much must Martin provide to fund this bequest?

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Business

Jaron Pierce

5 September, 20:48

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $ 9 comma 000 in the first year, and will grow by 5 % per year, forever. If the interest rate is 10 %, how much must Martin provide to fund this bequest?

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Elsa Foster · Answer 1

Present Value = $180,000

Explanation:

Giving the following information:

The bequest will provide $9,000 in the first year and will grow by 5 % per year, forever.

Interest rate = 10%

To calculate the present value of this perpetual annuity with a growing rate, we need to use the following formula:

PV = Cf / (i-g)

Cf = cash flow = 9,000

i = 0.10

g = 0.5

PV = 9,000 / (0.10 - 0.05) = $180,000