# Compounding

## What it is:

Compounding is the process of the exponential increase in the value of an investment due to earning interest on both principal and accumulated interest.

## How it works (Example):

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

Well, if the bank simply gave you 5% of your \$100 at the end of the year, you would have \$105 on December 31. If you left the \$105 in the account to earn another 5% next year, at the end of that second year, you would have: \$110.25 (\$105 x 1.05 = \$110.25). Not only did you earn interest on your original \$100 in year two, you earned interest on year one's interest. If you carried this out another eight years, here's what your account might look like:

Year    Beginning Balance    Interest Earned    Ending 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           \$147.75                         \$7.39                     \$155.13
10         \$155.13                         \$7.76                     \$162.89

If you had only earned interest on your original principal, and not on accrued interest payments, then you would have only \$150 at the end of 10 years. While this may not sound like much of a difference, imagine the effect with much larger balances, longer periods of time, and higher interest rates.

## Why it Matters:

Compounding is often referred to as "magic" because it is one of the most fundamental ways to build wealth, yet takes the least amount of effort. Given time, earning interest on interest can 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, an account which calculates and pays interest on a daily basis will grow faster than the same account calculating interest on a monthly basis.