# You have accumulated some money for your retirement. You are going to withdraw $92,645 every year...

## Question:

You have accumulated some money for your retirement. You are going to withdraw $92,645 every year at the beginning of the year for the next 19 years, starting today. Your account pays you 12.9% 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.

## Present value of annuity due:

The present value of annuity due is the present value of periodic payments to be received for a specified number of periods. It differs from ordinary annuity in a way that the payments are received at the beginning of each period rather than at the end.

## Answer and Explanation: 1

The present value of annuity due can be represented as:

{eq}PV= C+C\times \frac{1-(1+r)^{-(n-1)}}{r} {/eq}

Where:

C is the payment per period = $92,645

r is the rate per period = 12.9% or 0.129

n is the number of periods = 19

Substituting the values we have:

{eq}PV= $92,645 + ( $92,645 \times \frac{1-(1+0.129)^{-(19-1)}}{0.129}) {/eq}

{eq}PV= $ 92,645 + $ 637,316.88 {/eq}

{eq}PV= $ 729,961.88 {/eq}

Hence you must have accumulated $729,961.88

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Chapter 21 / Lesson 15An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.

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