# 6.4 Solve simple interest applications  (Page 2/8)

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Sean's new car loan statement said he would pay $\text{4,866.25}$ in interest from an interest rate of $\text{8.5%}$ over $5$ years. How much did he borrow to buy his new car?

$11,450 In $5$ years, Gloria's bank account earned $\text{2,400}$ interest at $\text{5%.}$ How much had she deposited in the account?$9,600

In the simple interest    formula, the rate of interest is given as an annual rate, the rate for one year. So the units of time must be in years. If the time is given in months, we convert it to years.

Caroline got $\text{900}$ as graduation gifts and invested it in a $\text{10-month}$ certificate of deposit that earned $\text{2.1%}$ interest. How much interest did this investment earn?

## Solution

We are asked to find the interest, $I.$

Organize the given information.

$\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{900}\hfill \\ \hfill r& =& \text{2.1%}\hfill \\ \hfill t& =& \text{10 months}\hfill \end{array}$

 Write the formula. $I=Prt$ Substitute the given information, converting 10 months to $\frac{10}{12}$ of a year. $I=900\left(0.021\right)\left(\frac{10}{12}\right)$ Multiply. $I=15.75$ Check your answer. Is $15.75 a reasonable amount of interest? If Caroline had invested the$900 for a full year at 2% interest, the amount of interest would have been $18. Yes,$15.75 is reasonable. Write a complete sentence that answers the question. The interest earned was $15.75. Adriana invested $\text{4,500}$ for $8$ months in an account that paid $\text{1.9%}$ interest. How much interest did she earn?$57.00

Milton invested $\text{2,460}$ for $20$ months in an account that paid $\text{3.5%}$ interest How much interest did he earn?

$143.50 ## Access additional online resources ## Key concepts • The formula $I=Prt$ can be used to calculate the amount of interest on an investment. See [link] . • By writing an equation based on information provided about simple interest, any value in the equation $I=Prt$ can be found. See [link] . ## Practice makes perfect Use the Simple Interest Formula In the following exercises, use the simple interest formula to fill in the missing information. Interest Principal Rate Time (years) $\text{1200}$ $\text{3%}$ $5$$180

Interest Principal Rate Time (years)
$\text{1500}$ $\text{2%}$ $\text{4}$

Interest Principal Rate Time (years)
$4410$ $\text{4.5%}$ $\text{7}$

$14,000 Interest Principal Rate Time (years) $2212$ $\text{3.2%}$ $\text{6}$ Interest Principal Rate Time (years) $577.08$ $\text{4580}$ $\text{2}$ 6.3% Interest Principal Rate Time (years) $528.12$ $\text{3260}$ $\text{3}$ In the following exercises, solve the problem using the simple interest formula. Find the simple interest earned after $5$ years on $\text{600}$ at an interest rate of $\text{3%.}$$90

Find the simple interest earned after $4$ years on $\text{900}$ at an interest rate of $\text{6%.}$

Find the simple interest earned after $2$ years on $\text{8,950}$ at an interest rate of $\text{3.24%}.$

$579.96 Find the simple interest earned after $3$ years on $\text{6,510}$ at an interest rate of $\text{2.85%}.$ Find the simple interest earned after $8$ years on $\text{15,500}$ at an interest rate of $\text{11.425%}.$$14,167

Find the simple interest earned after $6$ years on $\text{23,900}$ at an interest rate of $\text{12.175%}.$

Find the principal invested if $\text{656}$ interest was earned in $5$ years at an interest rate of $\text{4%}.$

$3,280 Find the principal invested if $\text{177}$ interest was earned in $2$ years at an interest rate of $\text{3%}.$ Find the principal invested if $\text{70.95}$ interest was earned in $3$ years at an interest rate of $\text{2.75%.}$$860

Find the principal invested if $\text{636.84}$ interest was earned in $6$ years at an interest rate of $\text{4.35%.}$

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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