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A rich relative has bequeathed you a growing perpetuity. The first payment will occur one year...

A rich relative has bequeathed you a growing perpetuity. The first payment will occur one year from now and will be $1,000. Each year after that, you will receive a payment on the anniversary of the previous payment that is 8% larger than the previous payment. This pattern of payments will go on forever. Assume that the interest rate is 12% per year.

a) What is today’s value of the bequest?

b) What is the value of the bequest immediately after the first payment is made?

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Answer #1

a. The today's value of the bequest is computed as shown below:

= Payment after one year / ( interest rate - growth rate )

= $ 1,000 / ( 0.12 - 0.08)

= $ 25,000

b. The value is computed as shown below:

= Today's value as computed in above part x (1 + growth rate)

= $ 25,000 x 1.08

= $ 27,000

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