Applications With Simple Interest
Learning Outcomes
- Calculate principal given rate, interest earned, and time
- Calculate the amount of interest earned given the rate, time and principal
- Calculate the interest rate given principal, time in months, and interest earned
- Determine how much was borrowed to buy a car given interest, rate and time
Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula. We will provide examples of how to find interest earned, calculate the rate of interest, and how to find the principal given a rate and the interest earned.
We will start by solving a simple interest application to find the interest.example
Nathaly deposited [latex]\text{\$12,500}[/latex] in her bank account where it will earn [latex]\text{4%}[/latex] interest. How much interest will Nathaly earn in [latex]5[/latex] years? Solution We are asked to find the Interest, [latex]I[/latex]. Organize the given information in a list. [latex-display]\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{$12,500}\hfill \\ \hfill r& =& \text{4%}\hfill \\ \hfill t& =& \text{5 years}\hfill \end{array}[/latex-display]Write the formula. | [latex]I=Prt[/latex] |
Substitute the given information. | [latex]I=\left(12,500\right)\left(0.04\right)\left(5\right)[/latex] |
Simplify. | [latex]I=2,500[/latex] |
Check your answer. Is [latex]\text{\$2,500}[/latex] a reasonable interest on [latex]\text{\$12,500}[/latex] over [latex]5[/latex] years? | |
At [latex]4\text{%}[/latex] interest per year, in [latex]5[/latex] years the interest would be [latex]20\text{%}[/latex] of the principal. Is [latex]20\text{%}[/latex] of [latex]\text{\$12,500}[/latex] equal to [latex]\text{\$2,500}[/latex]? Yes. | |
Write a complete sentence that answers the question. | The interest is [latex]\text{\$2,500}[/latex]. |
try it
[ohm_question]146792[/ohm_question]example
Loren lent his brother [latex]\text{\$3,000}[/latex] to help him buy a car. In [latex]\text{4 years}[/latex] his brother paid him back the [latex]\text{\$3,000}[/latex] plus [latex]\text{\$660}[/latex] in interest. What was the rate of interest?Answer: Solution We are asked to find the rate of interest, [latex]r[/latex]. Organize the given information. [latex-display]\begin{array}{ccc}\hfill I& =& 660\hfill \\ \hfill P& =& \text{$3,000}\hfill \\ \hfill r& =& ?\hfill \\ \hfill t& =& \text{4 years}\hfill \end{array}[/latex-display]
Write the formula. | [latex]I=Prt[/latex] |
Substitute the given information. | [latex]660=\left(3,000\right)r\left(4\right)[/latex] |
Multiply. | [latex]660=\left(12,000\right)r[/latex] |
Divide. | [latex]\frac{660}{12,000}=\frac{\left(12,000\right)r}{12,000}[/latex] |
Simplify. | [latex]0.055=r[/latex] |
Change to percent form. | [latex]\text{5.5%}=r[/latex] |
Check your answer. Is [latex]5.5\text{%}[/latex] a reasonable interest rate to pay your brother? | |
[latex]I=Prt[/latex] | |
[latex]660\stackrel{?}{=}\left(3,000\right)\left(0.055\right)\left(4\right)[/latex] | |
[latex]660=660\quad\checkmark [/latex] | |
Write a complete sentence that answers the question. | The rate of interest was [latex]5.5\text{%}[/latex]. |
try it
[ohm_question]146793[/ohm_question]example
Eduardo noticed that his new car loan papers stated that with an interest rate of [latex]\text{7.5%}[/latex], he would pay [latex]\text{\$6,596.25}[/latex] in interest over [latex]5[/latex] years. How much did he borrow to pay for his car?Answer: Solution We are asked to find the principal, [latex]P[/latex]. Organize the given information. [latex-display]\begin{array}{ccc}\hfill I& =& 6,596.25\hfill \\ \hfill P& =& ?\hfill \\ \hfill r& =& \text{7.5%}\hfill \\ \hfill t& =& \text{5 years}\hfill \end{array}[/latex-display]
Write the formula. | [latex]I=Prt[/latex] |
Substitute the given information. | [latex]6,596.25=P\left(0.075\right)\left(5\right)[/latex] |
Multiply. | [latex]6,596.25=0.375P[/latex] |
Divide. | [latex]\frac{6,596.25}{0.375}=\frac{0.375P}{0.375}[/latex] |
Simplify. | [latex]17,590=P[/latex] |
Check your answer. Is [latex]\text{\$17,590}[/latex] a reasonable amount to borrow to buy a car? | |
[latex]I=Prt[/latex] | |
[latex]6,596.25\stackrel{?}{=}\left(17,590\right)\left(0.075\right)\left(5\right)[/latex] | |
[latex]6,596.25=6,596.25\quad\checkmark [/latex] | |
Write a complete sentence that answers the question. | The amount borrowed was [latex]\text{\$17,590}[/latex]. |
TRY IT
[ohm_question]146794[/ohm_question]example
Caroline got [latex]\text{\$900}[/latex] as graduation gifts and invested it in a [latex]\text{10-month}[/latex] certificate of deposit that earned [latex]\text{2.1%}[/latex] interest. How much interest did this investment earn?Answer: Solution We are asked to find the interest, [latex]I[/latex]. Organize the given information. [latex-display]\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}[/latex-display]
Write the formula. | [latex]I=Prt[/latex] |
Substitute the given information, converting 10 months to [latex]\frac{10}{12}[/latex] of a year. | [latex]I=$900\left(0.021\right)\left(\frac{10}{12}\right)[/latex] |
Multiply. | [latex]I=15.75[/latex] |
Check your answer. Is [latex]\text{\$15.75}[/latex] a reasonable amount of interest? | |
If Caroline had invested the [latex]\text{\$900}[/latex] for a full year at [latex]2\text{%}[/latex] interest, the amount of interest would have been [latex]\text{\$18}[/latex]. Yes, [latex]\text{\$15.75}[/latex] is reasonable. | |
Write a complete sentence that answers the question. | The interest earned was [latex]\text{\$15.75}[/latex]. |
try it
[ohm_question]146796[/ohm_question]Licenses & Attributions
CC licensed content, Shared previously
- Determine the Amount of Interest Earned (Simple Interest). Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Determine a Simple Interest Rate For a Loan with Known Interest. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].