Compound interest seems very simple but leads to unpredictable results.  What could be simpler than multiplying a sum by one plus the interest rate?  For example, to get the value of an investment of \$10 at 5% interest after the first interest is received, simply multiply \$10 by 1.05 to get:  \$10 * (1.05) = \$10.50.  To find the value after the second payment, simply multiply \$10.50 by 1.05 and so on.

The odd thing about compound interest, however, is that in just a few periods the amounts can get very big.  I remember reading in a Richie Rich comic book as a boy where Richie’s friend gave a \$5 donation and Richie Rich offered to but give only 1 penny, and then to double it each day for 30 days.  His friend scoffed that such a rich boy would only give a penny.  The end of the comic, however, shows Richie Rich handing over a check for over a million dollars.  Amazingly, if you double 1 penny just thirty times, it is over a million dollars!

When saving and investing your initial efforts seem really pointless.  If you invest \$1000 in a mutual fund and make 10%, you get \$100 for the year.  It seems like that will never grow enough to replace your \$60,000 per year income.  Keep investing \$1000 per year, however, and the value would grow as follows:

Total Investment         Interest Collected        Total Account

Year 1:           \$1000                                    \$100                        \$1100

Year 2:          \$2000                                    \$210                       \$2310

Year 3:          \$3000                                    \$331                        \$3641

Year 4:          \$4000                                   \$464                        \$5105

Year 5:          \$5000                                    \$610                        \$6715

Year 6:          \$6000                                   \$772                         \$8487

Year 7:          \$7000                                    \$985                         \$10,472

Year 8:          \$8000                                   \$1147                         \$12,619

Year 9:          \$9000                                   \$1362                         \$14,981

Year 10:        \$10,000                                 \$1598                        \$17,579

So, after just 10 years, you have increased your account value to over \$17,000 while only investing \$10,000.  Your interest payments that you are receiving are more than the amount you are investing each year.  This is where your investment really starts to grow since you interest is compounding.  After a while, it will make little difference if you continue to invest at all since the interest you are receiving will be so large.

Compounding is a double-edged, sword, however.  If you borrow money, it may seem like the interest you are paying is almost nothing when the amount you owe is small.  Allow it to grow, however, little by little as you charge dinners out and trips to the mall, and you begin to pay interest on the interest.  Even as you make payments the amount you owe just keeps growing, and it seems pointless to even make payments.

If you are paying off debt, however, and not taking on any more debt, take heart.  While it may seem that your \$500 monthly payment makes almost no dent at all on the balance when you are starting, each time you make a payment and pay off some of the balance, the interest that accrues will decrease a little bit.  Just as with the investment account where it seemed like nothing was happening and then the value started to grow like crazy, it will seem like the debt is not decreasing at all and then suddenly your \$500 payments are having a bigger and bigger effect.

Also, as you pay off some of the smaller debts, you can use the payment that you are saving to pay more on the larger debts.  You may start out with only \$300 extra available when you start each month, but if you pay off a \$200 per month debt, you now have \$500 per month to attack the next debt with.  Before you know it, you’ll be paying \$2000 per month extra on your mortgage and knocking it out years early.

Another interesting effect is when you have a long-term debt like a 30-year mortgage.  If you  pay just a little extra at the beginning, you can reduce the amount you will ultimately pay by a lot.  If you pay extra at the end, however, it has little effect.  To use this, look at your mortgage payment and see how much is principle and how much is interest.  Each time you make a payment that exceeds the amount due by one interest payment, you reduce your loan by one month.

For example, at the start of a loan a \$1000 payment may be \$970 interest and only \$30 principle.  If you pay an extra \$30 (the principle amount), or \$1030 instead of the standard \$1000 payment, that will eliminate one payment from your loan early.  This means you will pay \$1000 less than you would.  Pay an extra \$100, and you may save \$3000.  This is because you are saving 30 years’ worth of compounding interest on that extra \$100.

Near the end of the loan, you may be paying \$900 in principle but only \$100 in interest with each payment.  Making extra payments makes little difference now because you would need to make \$1900 payments to just remove one month from your loan.