Given the following values, use the simple interest formula to find the remaining variable.
Round to the nearest cent.
months

Ask by Mcfarlane Ward. in the United States

Mar 30,2025

Question

Given the following values, use the simple interest formula $$ I=P r t $$ to find the remaining variable. Round to the nearest cent. $$ I=\$ 283.77, r=3.56 \%, t=7 $$ months

UpStudy AI · Accepted Answer

We are given:
- Interest: $$ I=\$283.77 $$
- Annual interest rate: $$ r=3.56\% $$ (which as a decimal is $$ 0.0356 $$)
- Time: $$ t=7 $$ months (which in years is $$ \frac{7}{12} $$ years)

The simple interest formula is
$$
I = P \, r \, t.
$$

We need to solve for $$ P $$. Rearranging the formula gives
$$
P = \frac{I}{r \, t}.
$$

Substitute the given values:
$$
P = \frac{283.77}{0.0356 \times \frac{7}{12}}.
$$

First, compute the denominator:
$$
0.0356 \times \frac{7}{12} = \frac{0.0356 \times 7}{12} = \frac{0.2492}{12} \approx 0.02076667.
$$

Then, calculate $$ P $$:
$$
P \approx \frac{283.77}{0.02076667} \approx 13664.69.
$$

Thus, the principal rounded to the nearest cent is:
$$
P \approx \$13,\!664.69.
$$
The principal $$ P $$ is approximately \$13,664.69.

Given the following values, use the simple interest formula to find the remaining variable.
Round to the nearest cent.
months

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