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# Saving & Investing - Head Matters

## 3. How Interest is Earned

### b. Compound vs. simple interest

As you saw in the video, can be very powerful and can make your money grow much faster. Let's go through the differences between simple and step by step.

Calculating Simple Interest:

Interest = Principal (amount of money you saved) x Rate (of interest being paid on your savings) x Time (in years)

For example, if you saved \$100 and earned 10% interest each year for 8 years, you would earn \$80 for a total of \$180.

Interest = \$100 (principal) x .1 (rate) x 8 (time) = \$80.

Adding the \$80 in earnings to your original \$100, you would have \$180.

Calculating Interest:

Suppose you put \$1,000 into an investment that earns 10 percent interest.  You leave it there for 10 years.  Using the calculation, you might expect to have interest earnings of \$1,000 on top of your original investment of \$1,000 or a total of \$2,000 in your account.

Interest = \$1,000 (principal) x .1 (rate) x 10 (time) = \$1,000.

Adding the \$1,000 in earnings to your original \$1,000, you would have \$2,000, right?

Maybe not. Most investments offer interest, which means that you would have more than that.  The return will be much higher because you earn interest not just on the original amount that you invested (the principal) but also on the interest you have already earned.  This is called compound interest.

Here’s how works.  Let’s assume that 10 percent interest is compounded annually.  This first year you earn \$100 in interest.  Now you have \$1,100.  The second year, you earn interest on \$1,100 (\$1,100 x .1 = \$110.). Now you have \$1,210.  Note, too, that time periods may vary and the shorter the time period, the more you earn.

Here's a table that shows ten percent interest earned on an initial \$100 investment, compounded annually:

 Year Simple Interest Adds Total Saving Simple Interest Compound Interst Adds Total Saving Using Compound Interest 1 \$10 \$110 \$10 \$110 2 \$10 \$120 \$11 \$121 3 \$10 \$130 \$12 \$133 4 \$10 \$140 \$13 \$146 5 \$10 \$150 \$15 \$161 6 \$10 \$160 \$16 \$177 7 \$10 \$170 \$18 \$195 8 \$10 \$180 \$19 \$214

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