Question
Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. \( \mathrm{p}=\$ 310, \mathrm{r}=7.25 \%, \mathrm{t}=2.75 \) years The simple interest is \( \$ \square \). (Round to the nearest cent as needed.)
Ask by West Mckenzie. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simple interest is \$61.81.
Solution
1. Write the formula for simple interest:
\[
I = P \times r \times t
\]
2. Substitute the given values:
- \( P = 310 \) dollars,
- \( r = 7.25\% = 0.0725 \) (as a decimal),
- \( t = 2.75 \) years.
\[
I = 310 \times 0.0725 \times 2.75
\]
3. Calculate the product step by step:
- First, calculate \( 310 \times 0.0725 \):
\[
310 \times 0.0725 = 22.475
\]
- Next, multiply by \( 2.75 \):
\[
22.475 \times 2.75 \approx 61.80625
\]
4. Round the result to the nearest cent:
\[
I \approx \$61.81
\]
The simple interest is \( \$61.81 \).
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Extra Insights
To determine the simple interest, you can use the formula: \[ I = P \times r \times t \] where \(I\) is the interest, \(P\) is the principal amount (\$310), \(r\) is the rate (7.25% or 0.0725), and \(t\) is the time in years (2.75 years). Plugging in the values, we get: \[ I = 310 \times 0.0725 \times 2.75 \] Calculating this: 1. Calculate \(310 \times 0.0725 = 22.475\) 2. Then, \(22.475 \times 2.75 = 61.18125\) Thus, rounded to the nearest cent, the simple interest is \( \$61.18 \).