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NY Regents Exam - Integrated Algebra: Help and Review25 chapters | 272 lessons | 12 flashcard sets

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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.

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.

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.

500 * .05 * 3 is 75. That means *I* = 75, and Karen earned $75 in interest in three years. That's like free money the bank paid her just for letting them hang on to her $500.

The same day Karen gets her $75 in interest, she finds out that her parents set up a savings bond for her that's come due. They'd put $1000 in a bond that earned 4% interest. It's now worth $1600. How long ago did they invest the money?

This time, we're missing the time. But we know the principal, $1000, and the interest rate, 4%. We also know the total interest. Be careful not to assume it's $1600. Note that that's the principal and the interest, or the total value after adding the two amounts together. So the interest is just 1600 - 1000, or 600.

Let's set up our equation. Again, it's *I = Prt*. We know that's 600 = 1000 *.04 * *t*. 1000 * .04 is 40. 600/40 is 15. So, *t* = 15. That means that investment was made 15 years ago.

So, $75 in interest, a $1600 savings bond...everything's coming up Karen! Later that same awesome day, Karen gets yet another surprise. Karen neglected to pay a bill four years ago for a magazine subscription she bought online. Apparently, she clicked 'bill me later' and then just sort of forgot about it. The subscription originally cost $30, but they claim she owes $120 now. Holy cow! What was the interest rate?

Let's find out. Here, we know the principal is $30. The time is 4 years. What about the interest? If she owes $120 now, then the interest is $90, or 120 - 30. Let's find that rate.

Our equation, *I = Prt* is 90 = 30 * *r* * 4. 30 * 4 is 120, and 90/120 is .75. That makes the interest rate a whopping 75%. Next time, Karen's going to read the fine print.

To summarize, we learned about calculating **interest**, or the money paid over time for invested **principal**. Principal refers to the original investment.

We used the formula *I = Prt*, where *I* is the interest earned, *P* is the principal, *r* is the interest rate, and *t* is the time in years.

We can use this formula to calculate the simple interest. We can also use it to find any one of the missing variables, such as time or the **interest rate**.

After you've completed this lesson, you'll be able to:

- Define interest and principal
- Differentiate between simple and compound interest
- Identify the formula to calculate simple interest

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NY Regents Exam - Integrated Algebra: Help and Review25 chapters | 272 lessons | 12 flashcard sets

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