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# Percent Equations

## Equations to solve for rates, totals, and parts.

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Simple Interest
Credit: Jinkazamah
Source: https://www.flickr.com/photos/jinkazamah/2315705263/

Kevin has just moved to a new city for a job. He needs furniture but doesn’t have enough money to buy everything he needs. The furniture salesman offers Kevin a store credit card. He can put the cost of the furniture on the card and pay it off over time. The interest rate on the card is 15%. Kevin buys 3,000 worth of furniture and puts it on the credit card. How much interest will Kevin pay if it takes him 3 years to pay off the balance? In this concept, you will learn to calculate the simple interest on a loan. ### Calculating Simple Interest Banks lend people money in the form of a loan. In return, the banks collect interest. Interest is the amount of money paid for the use of borrowed money. It is important to calculate the interest before taking a loan. One way is with simple interest. Simple interest is a quick way to calculate the interest of a loan. The formula for simple interest is: \begin{align*}\begin{array}{rcl} I & = & prt\\ \text{Interest} & = & \text{principal} \times \text{rate} \times \text{time} \end{array}\end{align*} The principal is the sum of money being borrowed. Interest rate is the percent of the principal you pay in addition to the principal over a time period. Interest rates are usually calculated annually, or per year. Time is the amount of time the borrower has agreed to pay back the loan. Let's look at an example. Carrie borrowed500 from the bank. The bank charges a 5% interest rate annually. If it takes Carrie 1 year to pay back the money, how much interest will she pay?

The principal is 500. The rate is 5% per year or 0.05. The time is 1 year. Let’s use the formula for simple interest. \begin{align*}\begin{array}{rcl} I & = & (500)(0.05)(1)\\ I & = & 25 \end{array}\end{align*} Carrie will pay25.00 in interest.

Calculate the interest had it taken Carrie 3 years to pay back the loan.

\begin{align*}\begin{array}{rcl} I & = & (500)(0.05)(3)\\ I & = & (25.00)(3)\\ I & = & \75.00 \end{array}\end{align*}

Carrie would have paid $75.00 in interest. ### Examples #### Example 1 Earlier, you were given a problem about Kevin’s furniture loan. Kevin bought$3,000 worth of furniture and put it on a credit card with a 15% interest rate. He takes 3 years to pay off the loan. To calculate the interest, use the formula: \begin{align*}I = prt\end{align*}.

Substitute in the given values.

\begin{align*}\begin{array}{rcl} I & = & (3,000)(0.15)(3)\\ I & = & 1,350 \end{array}\end{align*}

Kevin will pay $1,350 in interest. #### Example 2 Find the simple interest of the loan. Kelly saved$2500.00 in her savings account. Her annual interest rate was 3.5%. In four years, how much interest will Kelly’s account accumulate?

The principal is 2500. The rate is 3.5% per year or 0.035. The time is 4 years. Use the formula for simple interest. \begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (2500)(0.035)(4)\\ I & = & 350 \end{array}\end{align*} Kelly’s account will accumulate350.00 in interest.

#### Example 3

Mark borrowed 250.00 at 4% for 3 years. How much interest did he pay? Use the formula for simple interest. \begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (250)(0.04)(3)\\ I & = & 30 \end{array}\end{align*} Mark will pay30 in interest.

#### Example 4

Kris borrowed 300.00 at 2% for 2 years. How much interest did he pay? Use the formula for simple interest. \begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (300)(.02)(2)\\ I & = & 12 \end{array}\end{align*} Kris will pay12 in interest.

#### Example 5

Carmen has 1,200.00 in her savings account at 3% interest. In two years, how much interest will she accumulate? Use the formula for simple interest. \begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (1,200)(0.03)(2)\\ I & = & 72 \end{array}\end{align*} Carmen will pay72 in interest.

### Review

Find the simple interest on each amount.

1. $500.00 at 4% for 2 years 2.$200.00 at 5% for 3 years
3. $5000.00 at 2% for 2 years 4.$600.00 at 10% for 1 year
5. $1200.00 at 4% for 2 years 6.$1500.00 at 3% for 1 year
7. $2300.00 at 2% for 2 years 8.$500.00 at 4% for 2 years
9. $2500.00 at 5% for 5 years 10.$1500.00 at 11% for 2 years
11. $3500 at 3% for 5 years 12.$3500 at 4% for 15 years
13. $13,000 at 4.5% for 6 years 14.$23,000 at 3.5% for 10 years
15. \$50,000 at 2.5% for 20 years

To see the Review answers, open this PDF file and look for section 8.21.

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Color Highlighted Text Notes

### Vocabulary Language: English

Annually

An event occurs annually if it happens once per year.

Compound interest

Compound interest refers to interest earned on the total amount at the time it is compounded, including previously earned interest.

future value

In the context of earning interest, future value stands for the amount in the account at some future time $t$.

Percent

Percent means out of 100. It is a quantity written with a % sign.

present value

In the context of earning interest, present value stands for the amount in the account at time 0.

Simple Interest

Simple interest is interest calculated on the original principal only. It is calculated by finding the product of the the principal, the rate, and the time.