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].

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].

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].

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].