# You are 26 years old and decide to start saving for your retirement. You plan to save $5,500 at...

## Question:

You are 26 years old and decide to start saving for your retirement. You plan to save $5,500 at the end of each year (so the first deposit will be one year from now) and will make the last deposit when you retire at age 69.

a. Suppose you earn 6% per year on your retirement savings How much will you have saved for retirement?

b. How much will you have saved if you wait until age 39 to start saving (again, with your first deposit at the end of the year)?

## Saving for Retirement:

A common way to finance retirement is to make regular deposits into a saving account until the date of retirement. In this case, the series of deposits become an annuity, and the key piece of information is the future value of the deposits at retirement.

## Answer and Explanation: 1

a. The value will be $1,031,291.67.

We can use the following formula to compute the future value of an annuity with period payment {eq}M {/eq}, periodic interest {eq}r{/eq} for {eq}T{/eq} periods:

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

In this question, the annual saving is 5,500, and there will be 69 - 26 = 43 deposits. At the interest rate of 6%, applying the formula, the value at retirement is:

- {eq}\displaystyle \frac{5,500*((1 + 6\%)^{43} - 1 ) }{6\%} = 1,031,291.67 {/eq}

b. The value at retirement will be $434,820.02.

If you wait until you are 39 to make the first deposits, then there will be 69 - 39 = 30 deposits. Applying the formula again, the value at retirement will be:

- {eq}\displaystyle \frac{5,500*((1 + 6\%)^{30} - 1 ) }{6\%} = 434,820.02 {/eq}

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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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