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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?
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. | $I=\mathrm{\$900}(0.021)\left(\frac{10}{12}\right)$ |
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
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) |
---|---|---|---|
$\mathrm{\$4410}$ | $\text{4.5\%}$ | $\text{7}$ |
$14,000
Interest | Principal | Rate | Time (years) |
---|---|---|---|
$\mathrm{\$2212}$ | $\text{3.2\%}$ | $\text{6}$ |
Interest | Principal | Rate | Time (years) |
---|---|---|---|
$\mathrm{\$577.08}$ | $\text{\$4580}$ | $\text{2}$ |
6.3%
Interest | Principal | Rate | Time (years) |
---|---|---|---|
$\mathrm{\$528.12}$ | $\text{\$3260}$ | $\text{3}$ |
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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