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## How Your Money Can Grow

Making regular payments to yourself, even in small amounts, can add up over time. The amount your money grows depends on the interest earned and the amount of time you leave it in the account.

Interest is:

• An amount of money banks or other financial institutions pay you for keeping money on deposit with them
• Expressed as a percentage
• Calculated based on the amount of money in your account

#### Annual versus Daily Compounding

Compounding is how your money can grow when you keep it in a financial institution that pays interest.

When a financial institution compounds the interest in your account, you earn money on the previously paid interest, in addition to the money in your account.

Not all savings accounts are created equal. This is because interest can be compounded daily, monthly, or annually.

##### Annual Compounding

\$1,000.00 compounded annually at 1% earns you \$10.00 in interest at the end of the year. Interest is calculated once, at the end of the year. This gives you more money than if you had kept it under your mattress.

##### Daily Compounding

The more frequently interest compounds, the faster it grows. If you deposit \$1,000.00 in an account that has daily compounding, at the end of the day you would have \$1,000.03. The next day, the interest would be calculated based on the amount of your original deposit PLUS the previously earned interest, \$1,000.03, rather than just \$1,000.00. By the end of the year, you will have \$1,010.05.

 Annual Compounding Daily Compounding Start with \$1,000 at 1% compounded annually. At the end of the first day, you still have \$1,000. At the end of the year, you have \$1,010.00 - \$10.00, or 1% of \$1,000 is added to the original deposit. Start with \$1,000 at 1% compounded daily. At the end of the first day, you have \$1,000.03. On the second day, add the interest earned, \$0.03, and compounded the total amount - \$1,000.03. At the end of the year, you have \$1,010.05 from compounding each day's interest rate added to \$1,000. Total: \$1,010.00 Total: \$1,010.15

#### Compounding Interest Over Time

The extra \$0.05 does not seem like much, but it can add up over time.

 Type of Compounding 5 years 10 years Mattress compounding – NO interest! \$1,000 (unless stolen or lost) \$1,000 (unless stolen or lost) Annual compounding at 1% \$1,051.01 \$1,104.62 Monthly compounding at 1% \$1,051.25 \$1,105.12 Daily compounding at 1% \$1,051.27 \$1,105.17

#### Saving Money

You do not need \$1,000.00 to see the power of compounding. For example, let’s say a slice of pizza costs \$2.00, and you buy a slice every week for the next 50 years. You will spend \$5,200.00 (\$2.00 x 52 weeks x 50 years) on pizza and receive no interest.

However, if you had given up that slice of pizza and invested the money in an account earning 8% interest compounded, for example, you could have earned over \$64,578.87. Which would you rather have with that money – pizza that costs \$5,200.00 or more than \$64,000.00?

### Rule of 72

The rule of 72 is a formula that lets you estimate how long it will take for your savings to double in value. This calculation assumes that the interest rate remains the same over time. Here is how you calculate it:

• Divide 72 by the current interest rate to estimate the number of years that it will take to double your initial savings amount.
• For example, if you invest \$50.00 in a savings account at a 4% interest rate, it will take about 18 years for your initial savings of \$50.00 to double.
• 72 ÷ 4 = 18 years

You can also estimate the interest rate you would need to earn to double your money within a set number of years. Here is how you calculate it:

• Divide 72 by a certain amount of years to estimate the interest rate that it will take to double your initial savings amount.
• For example, if you put \$500.00 in an account that you want to double in 12 years, you will need an interest rate of 6%.