# How to Solve Interest Problems: Steps & Examples

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• 0:01 Calculating Interest
• 1:52 Finding the Interest
• 3:33 Finding the Time
• 4:34 Finding the Interest Rate
• 5:37 Lesson Summary

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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

If you want to know how your money can earn money, then it's essential to learn about solving interest problems. In this lesson, we'll practice calculating interest amounts and interest rates.

## Calculating Interest

It's great to have money. But what's even better? When your money earns more money just for being somewhere. It's like having rabbits as pets. Just having rabbits means you'll soon have more rabbits because rabbits multiply like, well, rabbits.

In this lesson, we're going to learn about interest. We can define interest as money paid over time for invested principal. When we say principal, we mean the original investment.

Here's Karen. She has some extra money that she's been storing in her sock drawer. That's fine, but she wants her money to work for her, so she's going to invest it. Let's say she invests \$500. That's the principal, or the original amount.

The money earned on top of the \$500 is the interest. We call the rate at which interest is earned the interest rate. I totally just defined interest rate by using the words 'interest' and 'rate,' but hopefully that one's pretty self-explanatory.

We can determine how much interest Karen will earn using this formula: I = Prt. Capital I stands for the interest. We use capital P to symbolize the principal. Lowercase r is the interest rate. We always convert the percent to a decimal; in other words, 8% becomes .08.

Finally, lowercase t is the amount of time. We typically use years as a measure of time, so if we're talking about one year, then t is 1.

To solve interest problems, we follow these steps. First, read the entire problem. Know what you're dealing with. Second, identify the question. Maybe you're trying to find the interest, or maybe it's the interest rate. This will be the variable in your equation that stays a variable. Third, identify the known values. You should be given most of the values. Find them and match them to the parts of your formula. Finally, solve for the missing values.

## Finding the Interest

Let's say that Karen invests her \$500 in an account that earns 5% interest. Whoa! Where's that bank? In Algebra City, a fictional place with amazing interest rates! Oh, nuts. Anyway: How much interest will she earn in three years?

To solve this problem, let's follow our steps. We read the problem. And we want to know the interest earned, which is I. Let's figure out what we know from our formula. We know the principal is \$500. The interest rate is 5%. And the time is three years.

I should note that we use this formula to calculate simple interest. That's what we'll do throughout this lesson. The opposite of simple interest is compound interest. Compound interest is a bit more complicated. This is what happens when the earned interest is added to the principal in set intervals, such as monthly, then the new interest is calculated off the new principal.

Imagine you have \$100 and, after a month, you earn \$5 in interest. With compound interest, we'd consider the principal to be \$105 for the second month. And the principal would continue to rise with each period.

But we're just focusing on the more straightforward simple interest, where the principal never changes during the period we're considering.

OK, back to Karen and her \$500. Let's set up our equation. Remember, it's I = Prt. We know the Prt is 500 * .05 * 3. That's principal times interest rate (as a decimal) times the time in years.

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