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Simple Interest

Use I = PRT to solve for principal, rate, time or interest.

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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: IInterest==prtprincipal×rate×time\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. II==(500)(0.05)(1)25\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.

III===(500)(0.05)(3)(25.00)(3)75.00\begin{align*}\begin{array}{rcl} I & = & (500)(0.05)(3)\\ I & = & (25.00)(3)\\ I & = & \75.00 \end{array}\end{align*} Carrie would have paid75.00 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: I=prt\begin{align*}I = prt\end{align*}. Substitute in the given values. II==(3,000)(0.15)(3)1,350\begin{align*}\begin{array}{rcl} I & = & (3,000)(0.15)(3)\\ I & = & 1,350 \end{array}\end{align*} Kevin will pay1,350 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.

III===prt(2500)(0.035)(4)350\begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (2500)(0.035)(4)\\ I & = & 350 \end{array}\end{align*}

Kelly’s account will accumulate $350.00 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.

III===prt(250)(0.04)(3)30\begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (250)(0.04)(3)\\ I & = & 30 \end{array}\end{align*}

Mark will pay $30 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.

III===prt(300)(.02)(2)12\begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (300)(.02)(2)\\ I & = & 12 \end{array}\end{align*}

Kris will pay $12 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.

III===prt(1,200)(0.03)(2)72\begin{align*}\begin{array}{rcl} I & = & prt\\ I & = & (1,200)(0.03)(2)\\ I & = & 72 \end{array}\end{align*}

Carmen will pay $72 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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Vocabulary Language: English

TermDefinition
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.