# You have accumulated some money for your retirement. You are going to withdraw $98,190 every year...

## Question:

You have accumulated some money for your retirement. You are going to withdraw $98,190 every year at the beginning of the year for the next 29 years starting from today. How much money have you accumulated for your retirement?

Your account pays you 6.64 per cent per year, compounded annually. (Hint: Find the present value of the cash flows.)

## Present Value of Annuity:

An annuity consists of a series of equal payments that are paid at a regular time interval. The present value of an annuity is a lump-sum amount today that is equivalent in terms of value to the annuity.

## Answer and Explanation: 1

The amount of money you have accumulated is $1,249,564.74.

The amount of money accumulated is equal to the present value o the future withdrawals, which represent 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}

In this question, the annual payment is 98,190, the annual discount rate is 6.64%, and there are 29 payments. Applying the formula, the present value of the annuity is:

- {eq}\displaystyle \frac{98,190(1 - (1 + 6.64\%)^{-29})}{6.64\%} = 1,249,564.74 {/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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