Simple interest only earns a fixed amount of interest based on the original principal amount. On the other hand, compound interest is calculated by taking the interest earned and adding it to the principal amount for the next interest earning period of time. Compound interest grows with each compounding period.

Here is a visual representation of the difference between simple interest and compound interest. Notice that in the simple interest images, the blocks representing interest always stay the same size. However, the blocks representing interest in the compound interest column get bigger with each period. This also makes the principal of the next period grow bigger as well.

We will start by just compounding one time per year, assuming that our rate is an annual rate.

**Annual Compound Interest Formula:**

\( A = P( 1 + r )^t \)

A = Amount (ending amount)

P = Principal (beginning amount)

r = Interest rate when compounding one time per year as a decimal

t = Time in years

Video Source (03:56 mins) | Transcript

The next video uses simple interest to show an example of how compound interest works.

Video Source (06;41 mins) | Transcript

The following video will show another example of using simple interest to calculate compound interest, this time using excel to do those calculations. Then it will introduce the compound interest formula, which makes these calculations much faster.

Video Source (08:13 mins) | Transcript

Compound interest adds the interest earned in the previous period to the principal amount, so the interest from previous periods also earns interest. This is an important tool to understand as it is used daily in loans, credit cards, and investments (including savings and some checking accounts). Spend the time you need to understand this principle because it will help you in your life.

### Practice Problems

**Use the information given in Question 1 to solve Questions 2 and 3:**

**Use the annual compound interest formula for the following questions:**

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