How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period

Economics May 27, 2021

How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period. A. $29729 B. $1,486.44 C. $1,635D8 $2 000 00

Expert Solution

Answer

B .

Explanation

Computation of Difference in Present Value of Perpetuity and Present Value of Annuity:

Present Value of Perpetuity = Amount / Interest Rate

= $1,000 / 0.10

= $10,000

Present Value of Annuity = P*{[1 - (1 + r)^-n] / r}

= $1,000*{[1 - (1 + 0.10)^-20] / 0.10}

= $8,513.56

Difference in Present Value of Perpetuity and Present Value of Annuity = $10,000 - $8,513.56 = $1,486.44

So, the correct option is B "$1,486.44".

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