# Compounding

## What it is:

Compounding refers to the exponentially increasing value of an investment due to the process of earning interest on previous interest payments.

## How it works (Example):

Let's assume you have \$100 to open a savings account at Bank XYZ on January 1. The annual interest rate is 5%.

At the end of the first year, you would have \$105. If you left the \$105 in the account to earn another 5% next year, you would have \$110.25 (\$105 x 1.05) at the end of the second year. You would have earned an additional \$5.25 in year two. The extra \$0.25 was earned on the previous years interest (\$5.00 * 0.05 = \$0.25).

If you carried this out another eight years, here's what your account would look like:

 Year Beg. Bal. Interest Balance 3 \$110.25 \$5.51 \$115.76 4 \$115.76 \$5.79 \$121.55 5 \$121.55 \$6.08 \$127.63 6 \$127.63 \$6.38 \$134.01 7 \$134.01 \$6.70 \$140.71 8 \$140.71 \$7.04 \$147.75 9 \$147.74 \$7.39 \$155.13 10 \$155.13 \$7.76 \$162.89

If you had only earned interest on your original principal, then you would have \$150 at the end of 10 years. If you had earned interest on the accrued interest as well, you would have earned an additional \$12.89 in the same time period. While this may not seem like much of a difference, the effect is much more significant with larger balances, longer periods of time, and higher interest rates.

## Why it Matters:

The financial world often refers to compounding as "magic" because it is the most fundamental way to build wealth. Given time, earning interest on interest will exponentially grow wealth.

Investors should also note the rate of compounding may be increased or decreased, depending on how often the interest amount is calculated and paid. The shorter the interval between interest calculations, the faster interest will accrue and vice versa. Thus, any account which calculates and pays interest on a daily basis will grow faster than the same account calculating interest on a monthly basis.