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A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $1000. Each year after that, on the anniversary of the last payment you will receive a payment that is 8% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 12% per year, What is today’s value of the bequest? What is the value of the bequest immediately after the first payment is made?

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ogorwyne

Answer:

1. $25,000

2. $27,000

Explanation:

1. In this first question you are required to calculate today’s value of the bequest

Present value = cash flow in one year/(r-g)

= 1000/(0.12-0.08)

= 1000/0.04

=$25,000

Today's value of the bequest is therefore $25,000.

2. In this second question you are required to find the value of the bequest immediately after the first payment is made

= [1000*(1+0.08)]/(0.12-0.08

= 1080/0.04

= $27,000

The value after the first payment is made is $27,000

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