How Compound Interest Works

Interest is the compensation paid by the borrower to the lender for the use of money as a percent or an amount. The concept of interest is the backbone behind most financial instruments in the world.

There are two distinct methods of accumulating interest, categorized into simple interest or compound interest.

Simple Interest

The following is a basic example of how interest works. Derek would like to borrow $100 (usually called the principal) from the bank for one year. The bank wants 10% interest on it. To calculate interest:

$100 × 10% = $10

This interest is added to the principal, and the sum becomes Derek’s required repayment to the bank one year later.

$100 + $10 = $110

Derek owes the bank $110 a year later, $100 for the principal and $10 as interest.

Compound Interest

Compounding interest requires more than one period. For the first year, we calculate interest as usual.

$100 × 10% = $10

This interest is added to the principal, and the sum becomes Derek’s required repayment to the bank for that present time.

$100 + $10 = $110

However, the year ends, and in comes another period. For compounding interest, rather than the original amount, the principal + any interest accumulated since is used. In Derek’s case:

$110 × 10% = $11

Derek’s interest charge at the end of year 2 is $11. This is added to what is owed after year 1:

$110 + $11 = $121

When the loan ends, the bank collects $121 from Derek instead of $120 if it were calculated using simple interest instead. This is because interest is also earned on interest.

The Rule of 72

Anyone who wants to estimate compound interest in their head may find the rule of 72 very useful. Not for exact calculations as given by financial calculators, but to get ideas for ballpark figures. It states that in order to find the number of years (n) required to double a certain amount of money with any interest rate, simply divide 72 by that same rate.

Example: How long would it take to double $1,000 with an 8% interest rate?

n = 72 / 8 = 9

It will take 9 years for the $1,000 to become $2,000 at 8% interest. This formula works best for interest rates between 6 and 10%, but it should also work reasonably well for anything below 20%.

Tax and Inflation Considerations

Some forms of interest income are subject to taxes, including bonds, savings, and certificate of deposits(CDs). Taxes can have very big impacts on the end balance.

Inflation is defined as a sustained increase in the prices of goods and services over time. As a result, a fixed amount of money will relatively afford less in the future. The average inflation rate in the U.S. in the past 100 years has hovered around 3%.

Tax and inflation combined make it hard to grow the real value of money. For example, in the United States, the middle class has a marginal tax rate of around 25%, and the average inflation rate is 3%. To maintain the value of the money, a stable interest rate or investment return rate of 4% or above needs to be earned, and this is not easy to achieve.