Suppose that you have inherited an annuity that will pay $1000 one year from now, A)...

Suppose that you have inherited an annuity that will pay $1000 one year from now,

A) And a payment that is 5% larger than the prior payment each of the next 49 years. Assuming that the first payment occurs exactly one year from now and that the annual opportunity cost of capital is 10%, What is the value of this annuity today? Round your final answer to two decimals.

B) Each of the following payments will be 5% larger than the prior payment. Assuming that the annual opportunity cost of capital is 10%, What is the value of this perpetuity today? Round your final answer to two decimals.

Expert Solution

A). The annuity referred to is a growing annuity with growth rate of 5% and interest rate (opportunity cost of capital) of 10%, for 50 years. Present value is $18,046.29 as follows:

B). Present value of a perpetuity with constant growth is PV= PMT/(r-g)

Where PMT= First payment (given as $1,000), g= Growth rate (given as 5% or 0.05) and r= interest rate (given as cost of capital 10%, or, 0.10)

Therefore, Present Value= $1,000/(0.10-0.05) = $1,000/(0.05) = $20,000

jeff jeffy answered 6 months ago

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