# Simple Interest

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Basics on the topic
**Simple Interest**

After this lesson, you will be able to compute for simple interest and compare which interest rates are better given periods of time.

The lesson begins by teaching you the definitions for important terms like loan, principal, and interest. It leads you to learn the formula for simple interest. It concludes by reminding you about how to compare interest rates.

Learn about simple interest by helping Harriet choose between two bank loans for her park’s repair needs.

This video introduces new concepts, notation, and vocabulary such as loan (amount of money that can be borrowed from a bank over a period of time); principal (the initial amount of money borrowed); the simple interest (the amount of money paid to the bank in addition to the principal) and the formula for simple interest (where interest is equal to the principal multiplied by the rate of interest in decimal form times the length of time).

Before watching this video, you should already be familiar with percent as part of a whole, specifically 100, conversion of percent to fractions or decimals and multiplication of real numbers.

After watching this video, you will be prepared to solve multi-step problems with other applications of percent such as discounts, commissions, compound interest, taxes, fees, increases, decreases, and percent of error.

Common Core Standard(s) in focus: 7.RP.A.3 A video intended for math students in the 7th grade Recommended for students who are 12 - 13 years old

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Transcript
**Simple Interest**

Otter This World is known for its otterly awesome rides, and the Otter Viking Ship is no different. Hark! That noise can only mean one thing, those pesky weasels are "making it rain" again. Uh-oh...this time the weasels have gone too far. They've broken the machine! Luckily, Harriet, the park manager, notices this on CCTV, and puts in a call to a couple banks to get a quote on a loan so she can replace the broken ride. She calls the 1st National Beaver Bank, and the 2nd National Beaver Bank. The business beaver from the 1st Beaver Bank informs Harriet that he has an offer of a loan with a simple interest rate of 10% per year. The teller from the 2nd Beaver Bank counters with an attractive offer of 7% simple interest over 6 months. In order for Harriet to choose the best loan, and save some money, she'll have to understand simple interest. Let's help Harriet avoid paying more interest on the loan than she has to... What's a loan? A loan is money you can borrow from a bank for a given time period. The initial amount of money you borrow is called the principal. Of course, you need to pay this principal back in addition to the simple interest. Simple interest is the money you pay the bank to borrow the money. Harriet is requesting $5,000 in principal from the banks. The beaver banker from the 1st National Beaver Bank is offering a simple interest rate of 10% per year, while the beaver banker from the 2nd National Beaver Bank is offering a simple interest rate of 7% per six months. To calculate simple interest, you simply need to multiply the principal by the interest rate (in decimal form) by the length of time. In short form, this is written simply as 'i' equals 'p' 'r' 't'. As we said before, you not only need to pay the bank back the principal, but also the interest for the period of time you borrowed the money. Regardless of which bank Harriet borrows from, the principal is $5,000. Now we need to convert both of the interest rates to decimal form by dividing each percentage by 100. We get 0.1 for the first beaver bank and 0.07 for the second. The first bank's time period is already a year, so we can simply substitute 'one' for 't'. Also, since we want to compare the two interest rates, we should convert the second bank's time into years. Because 6 months happens twice a year we have to multiply the percentage, 0.07, by 2. If we plug in the numbers and multiply, we see that the interest owed to the first beaver bank at the end of a year is $500 and $700 for the second beaver bank. Great, let's review what we've learned. Harriet needs to get a loan from one of two beaver banks. The principal amount is $5,000. The simple interest rate from the 1st National Beaver Bank is 10% per year, which we calculated to be $500. The simple interest rate from the 2nd National Beaver Bank is 7% per 6 months, which sounds better at first, but which we calculated to be $700 per year. So if Harriet chooses the loan from the 1st bank with the 10% simple interest rate, she would owe the bank $5,500 at the end of the year. But if she chooses the 2nd Beaver Bank with the 7% simple interest over 6 months, she'd owe the bank $5,700 at the end of the year! Remember! If you want to compare two rates, make sure the time interval and units are the same! Sometimes, you might have to convert just like we did with the second bank's rate of 7% every 6 months. We can save Harriet $200 a year by going with the first beaver's offer! To find simple interest, you must multiply the principal times the decimal form of the rate, multiplied by the time in years. Harriet receives word that the repairs are done. And she scurries down to see the newly-repaired ride. Time for the big reveal... Let's see the new Otter Viking Ship! What in the world...!?!? Those weasels! What is this weasely ship?!