# You have accumulated some money for your retirement. You are going to withdraw $99790 every year...

## Question:

You have accumulated some money for your retirement. You are going to withdraw $99,790 every year at the beginning of the year for the next 20 years, starting today. Your account pays you 9.1 percent per year, compounded annually. How much money have you accumulated for your retirement? To answer this question, you have to find the present value of the cash flows. Round the answer to two decimal places.

## Annuity Due:

An annuity is a stream of payments of equal amount that occur at a regular time interval. If the first payment is made in the next period, the annuity is called an ordinary annuity. If the fist payment is instead paid today, the annuity is called an annuity due.

## Answer and Explanation: 1

You have accumulated $ 986,791.08 for your retirement.

The amount of money you have accumulated is the present value of your future withdrawals, discounted at the rate of return. In this case, the stream of withdrawals constitute an annuity. Moreover, since the first payment is made today, the annuity is an annuity due. We can use the following formula to compute the present value of an annuity due:

- {eq}\displaystyle \frac{M*((1 + r) - (1 + r)^{1-N})}{r} {/eq}

where {eq}M{/eq} is the periodic payment, {eq}r{/eq} is the periodic rate of return, {eq}N{/eq} is the number of payments.

Applying this formula, the present value of the future withdrawals is:

- {eq}\displaystyle \frac{99,790*((1 + 9.1\%) - (1 + 9.1\%)^{1-20})}{9.1\%} = 986,791.08 {/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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