# You have accumulated some money for your retirement. You are going to withdraw $61,746 every year...

## Question:

You have accumulated some money for your retirement. You are going to withdraw $61,746 every year at the end of the year for the next 28 years.

How much money have you accumulated for your retirement? Your account pays you 11.89% per year, compounded annually.

## Present Value of Annuity:

The present value of annuity is the lump sum equivalent individuals are willing to take today in exchange for the stream of future payments. The present value declines with the discount rate, but increases with the annuity payment and the length of the annuity.

## Answer and Explanation: 1

The amount of money you have accumulated is the present value of the future withdrawals. 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 amount of money you have accumulate is:

- {eq}\displaystyle \frac{61,746(1 - (1 + 11.89\%)^{-28})}{11.89\%} = 496,960.665 {/eq}

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Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.

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