# The Power ofCompound Interest

Most of us would like to have a good amount of money at some point in our life. What little amount we save while we work can and will accumulate over the years, but for most of us, the odds of reaching an exuberant amount of money (say \$1 million) seem relatively small. However, if we consider the power of compound interest, then maybe we can begin to realize this goal.

For example, let's say that you decide to invest \$100 per month for the next 30 years in a mutual fund that yields an average of 6% interest compounded monthly. In the end, you would have over \$100,000! That's not too bad, considering you'd have almost \$65,000 in money you didn't have before. Now, let's say you kept that up for another 10 years. Would you believe that you'd almost double that value and have almost \$200,000? I find that teachers don't emphasize this concept enough. If they did, we may have more millionaires at 60 than we do now. Think about it: you're 18 years old and you decide to invest \$67.00 per month (that's about \$2.20 per day). If you averaged a 12% return on that investment, you would have a cool \$1 million by the time you're 60. Imagine retiring at 60 with a million bucks! Even better: let's say you continued with this plan for just 5 more years. Incredibly, you'd have close to \$2 million! In just 5 more years, you almost make another million and double your investment.

There are two formulas we can use to help us with compound interest: one for annuities (regular investments over a period of time) and one for one-time investments. They are fairly straightforward: we substitute values for the variables in the formulas and the result is the future value of our investment. But I'm a curious person, so just finding out how much money I should have after a period of time is not enough for me. What if I want to know how long it will take me to have \$1 million if I invest \$100 per month? What if I want to know how much I should invest monthly to have \$200,000 in 25 years? What if I want to know what kind of interest rate I need in order to have \$500,000 in 35 years, if I invest \$150 per month? In order to answer these questions, I had to solve the formulas for the different variables in each. The solutions require knowledge of algebra, but if you're interested, you can take a look at step-by-step solutions of the one-time investment formula and the annuity formula for each of the variables.

NOTE:Around August of 2001, I received an e-mail stating that the formulas I use are wrong; that a \$10,000 one-time investment at 6% compounded monthly should yield around \$20,000 in one year. Of course this is not correct (it would be one hell of an investment opportunity if it was). I believe this was due to confusion as to what compounded monthly means. You can check out my reply if you wish.

## THE VARIABLES

• FV = future value
• a = one-time investment (one-time investment formula)
• p = investment per compound period (annuity formula)
• i = interest rate
• c = number of compound periods per year
• n = number of compound periods for the length of the investment

INSIGHTS:To get p, take the amount you want to invest per month, multiply it by 12 to get a yearly investment amount, and then divide by c to get the investment per compound period. For example, if you want to invest \$50 per month compounded quarterly (4 times per year): 50 * 12 = \$600 per year; 600 ÷ 4 = \$150 per compound period. In the form below, you're asked to specify monthly investments, not investment per compound period (p). The form will convert this for you automatically.

To get n, take the length of time you want to invest (in years), and multiply it by c to get the number of compound periods. For example, if you want to invest for 25 years compounded monthly (12 times per year): 25 * 12 = 300 compound periods for the length of the investment. In the form, you're asked to specify the number of years, not the number of compound periods (n). This will also be calculated for you automatically.

## THE FORMULAS

The formula to calculate the future value (FV) of a one-time investment (a) at i% interest compounded c times per year for n compound periods (over the length of the investment) is given as:

The formula to calculate the future value (FV) of a periodic investment (p) at i% interest compounded c times per year for n compound periods (over the length of the investment) is given as:

REMINDER:If you're interested, you can take a look at step-by-step solutions for the different variables of both the one-time and periodic investment formulas.

## PUTTING IT INTO PRACTICE

The form below allows you to input your own values. Clicking on a label (or radio button) selects the variable you want to solve for. You can also switch from one-time investment calculations to annuities. Bear in mind that these calculations are approximate. They are based on a fixed interest rate and fixed periodic investments (if determining the future value of an annuity).

NOTE:Solving for number of compound periods per year (c) is essentially useless. There's virtually no difference in the future value (FV) of an investment (one-time or periodic) whether it's compounded monthly, quarterly, or even daily.

 Type of investment: One-time investmentPeriodic investments (annuity) Solve for: Investment [a]: Monthly investment [will be converted to p]: Percent interest rate [i]: Number of times compounded each year [c]: Number of years [will be converted to n]: Future value [FV]:

## A FINAL NOTE

I hope it's clearly evident that compound interest can truly be powerful. There's no denying that it takes money to make money, but the potential to attain huge gains utilizing this power is there. My hope is that you receive something from my efforts. If you have any questions, criticism or suggestions, feel free to send them my way. Use this information and enjoy it, but above all, share it with someone else!