A wealthy woman just died and left her pet cats the following estate: $30,000 per year for the...

Question:

A wealthy woman just died and left her pet cats the following estate: $30,000 per year for the next 15 years with the first cash flow one year from today. At a discount rate of 2%, what is the feline estate worth in today's dollars?

Present Value of Annuity:

An annuity consists of a stream of equal payments, with a constant time interval between two consecutive payments. The present value of an annuity is the amount today that an individual would view as equivalent to the annuity.

Answer and Explanation:

The value today is $385,477.90.

The worth today is the present value of the cash flows from estate, which is an annuity. We can use the following formula to compute the present value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

  • {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}

Applying the formula, the present value of the annuity is:

  • {eq}\displaystyle \frac{30,000(1 - (1 + 2\%)^{-15})}{2\%} = 385,477.90 {/eq}

Learn more about this topic:

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How to Calculate the Present Value of an Annuity

from Business 110: Business Math

Chapter 8 / Lesson 3
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