Compound 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.

*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**

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:

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!

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Copyright © 2003, Jean Gourd (Jean.Gourd@usm.edu)