# At the age of 33, to save for retirement, you decide to deposit $80 at the end of each month in...

## Question:

At the age of 33, to save for retirement, you decide to deposit $80 at the end of each month in an IRA that pays 4.4% compounded monthly.

A. You will have approximately $ _____ in the IRA when you retire.

B. The interest is approximately $ _____?

## IRA:

Individual retirement account (IRA) is an important retirement saving vehicle. The current tax laws provide incentive for retirement saving by exempting eligible contributions to IRA from income tax.

## Answer and Explanation: 1

A. We can use the following formula to compute the future 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 + r)^T - 1)}{r} {/eq}

Suppose you retire at the age of 65, there will be 32 years of contribution (384 monthly contribution). Applying the formula, the amount in your IRA account is:

- {eq}\displaystyle \frac{80((1 + 4.4\%/12)^{384} - 1)}{4.4\%/12} = 67,140.20 {/eq}

B. The total interest earned = 67,140.20 - 80 * 384 = 36,420.20.

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Chapter 5 / Lesson 16Understand the definition of future value and the future value formula. Explore some examples that show how to calculate the future value of an investment.

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