## How long will it take to save a million dollars?

A million dollars is a large sum of money and depending where you are in your career, it may seem completely out of reach. If you use an investment vehicle, such as a 401(k), you might find that you are a lot closer to achieving this goal than you think, even if you start today! How will you reach your goal? Compound interest is the answer! Compound interest is the addition of interest to principal, whereby interest earned begins to yield interest in subsequent years of the investment.

## Compound Interest

Let’s take a look at the formula used to compute compound interest for one year. To simplify the calculation, interest will only be paid once at the start of the year:

`$, after n years = $, principal × (1 + annual interest rate)`

^{n}

To calculate the return on principal for the maximum contribution allowed by the Internal Revenue Service, $18,000, assuming a 5% compound annual interest rate, we can use the following formula to calculate the value after 1 year:

`$18,900 = $18,000 × (1 + .05)`

^{1}

Now that we have the basic formula for compound interest for one year, we can extrapolate this calculation for several years and compute how many years it will take to earn a million dollars using today’s maximum deferral limit for a 401(k) plan as set forth by the IRS.

`$, after n years = $, principal × (1 + annual interest rate)`

^{n} + $, annual contribution ×

`((1 + annual interest rate)`

^{(n + 1)} – (1 + annual interest rate)) / annual interest rate

`$1,030,046.38 = $18,000 × (1 + .05)`

^{26} + $18,000 × ((1 + .05)^{(26+1)} − (1 + .05)) / .05

In 26 years, you will have saved over one million dollars and will be well on your way to a happy and relaxing retirement. A small investment today can make a big difference tomorrow.