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Operations with Percents: Simple Interest & Percent Change

Instructor: Jeff Calareso

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

In this lesson, we'll learn how simple interest can earn (or cost) you money. We'll also look at percent change problems to better understand how discounts and markups work.

Percent Operations in the Real World

Few things you'll learn in math are as useful as operations with percents. Once you understand concepts like simple interest and percent change, you'll have knowledge that can literally put money in your pocket.

Simple interest is just what it sounds like: an easy way of calculating how much interest you can earn (or owe). Let's say you put some money in the bank and it's earning interest. The money you start with is your principal. The word 'principal' also means first, so this money is where your investment starts. Simple interest is a way of calculating just how much money your principal is earning you.

Percent change is closely related. Every time you see a sale advertising '30% off!' or if you want to leave a 20% tip at a restaurant, you're dealing with percent change. As with simple interest, you start with a principal amount. The percent change is the amount that principal increases or decreases. Let's look at examples of both of these ideas.

Simple Interest Formula

Let's start with simple interest. What if you deposit $500 and you'll earn 4% interest over 3 years. To calculate how much money your principal investment will earn you, we need a formula: I = prt.

I is for interest, of course. That's what we want to find. To get it, we just need to know three things: what we start with (the principal, or p), the interest rate (r) and the time (t) the money needs to sit.

Here, the principal is $500, the rate is 4% (or .04) and the time is 3 years. If we plug that into I = prt, we get I = (500)(.04)(3). That gets us $60. So you can earn $60 just by letting your money sit around for 3 years.

Sometimes, simple interest doesn't get you money, it costs you money. Imagine you borrow $800 from your friend Steve to help you buy a life-size statue of Bigfoot. You'd use your own money, but remember that it's locked away earning that 4% interest. This statue is a weird investment, but it's great of Steve to help. Well, not that great. You promise to pay Steve back in 2 years, but he'll charge you 7% interest.

To find out how much you'll need to pay Steve back, use the same formula: I = prt. This time, the principal is $800, the interest rate is 7% (or .07) and the time is 2 years. So that's I = (800)(.07)(2). That gives us $112.

But that's not what you owe Steve. If you recall, the formula you just used was to find the interest. You owe Steve the $112 interest plus the original $800. So the amount you'll have to pay back is $800 + $112, or $912. But, you know, life-size Bigfoot statue!

Percent Change

You're expecting your Bigfoot statue to go up in value. The guy who sold it to you said it should be worth 30% more than you paid for it. That's great! But how much is that in cold, hard cash? You paid $800 of your money… well, Steve's money. What is 30% more than $800?

This is a percent change problem. Since we want to find out what 30% more than our principal is, we're essentially figuring out what 130% of $800 is. (Remember, 100% of $800 is just $800.) 130% can be written as 1.30. To find the projected value of your statue, we multiply: $800 * 1.3. This gets us $1040. That's a nice increase!

Note that this is the same way you'd calculate a tip. If a check comes for $32 and you want to leave a 20% tip, just multiply $32 * 1.20 to get $38.40. That's the principal plus the tip.

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