# You have accumulated some money for your retirement. You are going to withdraw $74,959 every year...

## Question:

You have accumulated some money for your retirement. You are going to withdraw $74,959 every year at the beginning of the year for the next 16 years starting from today. How much money have you accumulated for your retirement? Your account pays you 13.41 percent per year, compound annually.

## Value of Annuity:

An annuity is series of periodic payments or receipts that are expected to occur at the end or at the beginning of every period. The equivalent present value of an annuity is dictated by the number of periodic payments and the applicable annual interest rate.

## Answer and Explanation: 1

The calculated money that is accumulated for retirement is **549,287.81**.

The present value of the 15 annual withdrawals starting from the beginning of next year is given by:

{eq}P\, = \dfrac{1\, -\, \left ( 1\, +\, i \right )^{-n}}{i}\times R {/eq}

Where;

R = annual withdrawal = $74,959

i = interest rate = 13.41%

P = Present value of 15 annual withdrawals

n = number of payments = 15

{eq}P\, = \dfrac{1\, -\, \left ( 1\, +\, 13.41\% \right )^{-15}}{13.41\%}\times 74,959 {/eq}

{eq}P = $474,328.81 {/eq}

The money accumulated for retirement is given by:

{eq}\begin{align*} &= \text{First withdrawal at the beginning of this year + present value of 15 annual withdrawals that start from the beginning of next year} \\[0.3 cm] &= $74,959 + $474,328.81 \\[0.3 cm] &= $549,287.81 \end{align*} {/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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