## What is compounding interest?

Lets start off with the basics. Interest typically refers to the money you receive at regular intervals in exchange for loaning your money out for a predetermined period of time, this could be in the form of a bond, commercial paper, T-bill, or even a GIC.

### Lets see how this comes to life with a real world example.

If you buy a  \$1000, 10-year corporate bond that has a coupon rate of 10% (pays 10 percent interest per year) you will receive \$100 per year for 10 year period. This will leave you with \$2000 after the 10 year period has expired, 10 interest payments of 100\$, and the principle repayment of 1000\$. Note that this is assuming that the corporation does not default on the bond, this occurs when a corporation declares bankruptcy and does not have enough liquid assets to ensure the price of the bond (a very real risk).

If however, you reinvest the interest payments when they are received, you will be gaining interest on the reinvested interest payments. If we reinvest the interest payments for the 10-year bond discussed above, the interest payment received in the first year would be \$100. Assuming you reinvest this money, and that of all subsequent interest payment you receive, in the second year you would receive an interest payment of \$110. In the third you would receive \$120.1, in the fourth year you would receive \$132.1, in the fifth year the interest payment would be \$146.2, in the sixth year it would be 160.8, in the seventh \$176.9, in the eight year \$194.6, in the ninth it will be \$214.1, and finally the last interest payment you receive would be for  \$235.5.

Your accumulated total at the end of the 10 year will amount to \$2590.3. A much more enticing sum than the \$2000 you would receive if interest payment are not reinvested. This is the miracle of compounding interest in action.

### The formula

The process we went through above is quite extensive, and unnecessary if you are only concerned with the sum you will receive after 10-years. The following formula can be used as a shortcut which tells you what your investment will be worth if you allow your interest payments to compound.

The total accumulated value, including the principal sum P plus compounded interest I, is given by the formula:

Where:

• P is the original principal sum
• P’ is the new principal sum
• r is the nominal annual interest rate
• n is the compounding frequency
• t is the overall length of time the interest is applied (usually expressed in years).

The total compounded interest is

### How to ensure you take advantage of the miracle of compounding

Obvious though it may seem, due to the importance of compounding interest payments it is worth stressing. For fixed income securities, this means reinvesting your interest payments into the fixed investment security, whatever it may be. It is important to note that the interest rate you receive when you reinvest your interest payments may be greater or less than the rate you received when purchasing the security, as such, the formula for compounding interest merely serves as a rough estimate of the sum you can expect at the end of the period.

For index funds and mutual funds, taking advantage of compounding interest is easy, all you have to do is select to have your dividends reinvested when you deposit money into the fund.

For individual stocks it is slightly more difficult, the only way to ensure that you get the full benefit of the magic that is compounding interest is to set up a dividend reinvestment (DRIP) account. This will buy whatever fraction of the stock for which you received a dividend payment that has an equivalent value to the dividend payment when the payments was received. This has the same effect as in the example on bonds, and can serve to greatly magnify your dividend returns, however an additional side effect of dividend reinvestment in stocks is that it also serves to magnify your capital gain or loss that you incur when you end up liquidating your position.

I’ll leave you with this final thought. The earlier you start saving and investing your money, the more time your interest has to compound, and the more money you will have at the end of the period.

Do you want to drive a Honda Civic or a Rolls Royce when you retire? The choice is yours my friends, save away!