# 6.4 Solve simple interest applications

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By the end of this section, you will be able to:
• Use the simple interest formula
• Solve simple interest applications

Before you get started, take this readiness quiz.

1. Solve $0.6y=45.$
If you missed this problem, review Decimals and Fractions .
2. Solve $\frac{n}{1.45}=4.6.$
If you missed this problem, review Decimals and Fractions .

## Use the simple interest formula

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal , $P,$ and the bank pays you interest , $I.$ The interest is computed as a certain percent of the principal; called the rate of interest , $r.$ The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, $t,$ represents the number of years the money is left in the account.

## Simple interest

If an amount of money, $P,$ the principal, is invested for a period of $t$ years at an annual interest rate $r,$ the amount of interest, $I,$ earned is

$I=Prt\phantom{\rule{2em}{0ex}}$

where

$\begin{array}{ccc}\hfill I& =& \text{interest}\hfill \\ \hfill P& =& \text{principal}\hfill \\ \hfill r& =& \text{rate}\hfill \\ \hfill t& =& \text{time}\hfill \end{array}$

Interest earned according to this formula is called simple interest    .

The formula we use to calculate simple interest is $I=Prt.$ To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Find the simple interest earned after $3$ years on $\text{500}$ at an interest rate of $\text{6%.}$

## Solution

Organize the given information in a list.

$\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{500}\hfill \\ \hfill r& =& \text{6%}\hfill \\ \hfill t& =& \text{3 years}\hfill \end{array}$

We will use the simple interest formula to find the interest.

 Write the formula. $I=Prt$ Substitute the given information. Remember to write the percent in decimal form. $I=\left(500\right)\left(0.06\right)\left(3\right)$ Simplify. $I=90$ Check your answer. Is $90 a reasonable interest earned on$500 in 3 years? In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes,$90 is reasonable. Write a complete sentence that answers the question. The simple interest is $90. Find the simple interest earned after $4$ years on $\text{800}$ at an interest rate of $\text{5%.}$$160

Find the simple interest earned after $2$ years on $\text{700}$ at an interest rate of $\text{4%.}$

$56 In the next example, we will use the simple interest formula to find the principal. Find the principal invested if $\text{178}$ interest was earned in $2$ years at an interest rate of $\text{4%.}$ ## Solution Organize the given information in a list. $\begin{array}{ccc}\hfill I& =& \text{178}\hfill \\ \hfill P& =& ?\hfill \\ \hfill r& =& \text{4%}\hfill \\ \hfill t& =& \text{2 years}\hfill \end{array}$ We will use the simple interest formula to find the principal.  Write the formula. $I=Prt$ Substitute the given information. $178=P\left(0.04\right)\left(2\right)$ Divide. $\frac{178}{0.08}=\frac{0.08P}{0.08}$ Simplify. $2,225=P$ Check your answer. Is it reasonable that$2,225 would earn $178 in 2 years? $I=Prt$ $178\stackrel{?}{=}2,225\left(0.04\right)\left(2\right)$ $178=178✓$ Write a complete sentence that answers the question. The principal is$2,225.

Find the principal invested if $\text{495}$ interest was earned in $3$ years at an interest rate of $\text{6%.}$

$2,750 Find the principal invested if $\text{1,246}$ interest was earned in $5$ years at an interest rate of $\text{7%}.$$3,560

Now we will solve for the rate of interest.

Find the rate if a principal of $\text{8,200}$ earned $\text{3,772}$ interest in $4$ years.

## Solution

Organize the given information.

$\begin{array}{ccc}\hfill I& =& \text{3,772}\hfill \\ \hfill P& =& \text{8,200}\hfill \\ \hfill r& =& ?\hfill \\ \hfill t& =& \text{4 years}\hfill \end{array}$

We will use the simple interest formula to find the rate.

 Write the formula. $I=Prt$ Substitute the given information. $3,772=8,200r\left(4\right)$ Multiply. $3,772=32,800r$ Divide. $\frac{3,772}{32,800}=\frac{32,800r}{32,800}$ Simplify. $0.115=r$ Write as a percent. $\text{11.5%}=r$ Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years? $I=Prt$ $3,772\stackrel{?}{=}8,200\left(0.115\right)\left(4\right)$ $3,772=3,772✓$ Write a complete sentence that answers the question. The rate was 11.5%. #### Questions & Answers what does nano mean? Anassong Reply nano basically means 10^(-9). nanometer is a unit to measure length. Bharti do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment? Damian Reply absolutely yes Daniel how to know photocatalytic properties of tio2 nanoparticles...what to do now Akash Reply it is a goid question and i want to know the answer as well Maciej characteristics of micro business Abigail for teaching engĺish at school how nano technology help us Anassong Do somebody tell me a best nano engineering book for beginners? s. Reply what is fullerene does it is used to make bukky balls Devang Reply are you nano engineer ? s. fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball. Tarell what is the actual application of fullerenes nowadays? Damian That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes. Tarell what is the Synthesis, properties,and applications of carbon nano chemistry Abhijith Reply Mostly, they use nano carbon for electronics and for materials to be strengthened. Virgil is Bucky paper clear? CYNTHIA so some one know about replacing silicon atom with phosphorous in semiconductors device? s. Reply Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure. Harper Do you know which machine is used to that process? s. how to fabricate graphene ink ? SUYASH Reply for screen printed electrodes ? SUYASH What is lattice structure? s. Reply of graphene you mean? Ebrahim or in general Ebrahim in general s. Graphene has a hexagonal structure tahir On having this app for quite a bit time, Haven't realised there's a chat room in it. Cied what is biological synthesis of nanoparticles Sanket Reply what's the easiest and fastest way to the synthesize AgNP? Damian Reply China Cied types of nano material abeetha Reply I start with an easy one. carbon nanotubes woven into a long filament like a string Porter many many of nanotubes Porter what is the k.e before it land Yasmin what is the function of carbon nanotubes? Cesar I'm interested in nanotube Uday what is nanomaterials​ and their applications of sensors. Ramkumar Reply what is nano technology Sravani Reply what is system testing? AMJAD preparation of nanomaterial Victor Reply how to synthesize TiO2 nanoparticles by chemical methods Zubear what's the program Jordan ? Jordan what chemical Jordan how did you get the value of 2000N.What calculations are needed to arrive at it Smarajit Reply Privacy Information Security Software Version 1.1a Good Jeannette has$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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