Question

a print shop borrows $2900 from a credit union for 231 days. the credit union charges simple interest at an annual rate of 8.25% for this loan. assume each day is \LXI0 of a year. answer each part below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find the interest that will be owed after 231 days. $\square$ (b) assuming the print shop doesnt make any payments, find the amount owed after 231 days. $\square$

Explanation:

Part (a)

Step1: Recall simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.

Step2: Identify values

• Principal ($P$) = $\$2900$
• Annual rate ($r$) = $8.25\% = 0.0825$ (converted to decimal)
• Time ($t$) = $\frac{231}{365}$ years (since each day is $\frac{1}{365}$ of a year)

Step3: Calculate interest

Substitute the values into the formula:
$I = 2900 \times 0.0825 \times \frac{231}{365}$

First, calculate $2900 \times 0.0825 = 239.25$

Then, multiply by $\frac{231}{365}$:
$I = 239.25 \times \frac{231}{365}$

Calculate $239.25 \times 231 = 55266.75$

Then divide by $365$:
$I = \frac{55266.75}{365} \approx 151.4157534$

Round to the nearest cent: $I \approx \$151.42$

Part (b)

Step1: Recall amount formula for simple interest

The amount owed ($A$) is the principal plus the interest, so $A = P + I$.

Step2: Substitute values

We know $P = \$2900$ and $I \approx \$151.42$ (from part a).

So, $A = 2900 + 151.42 = 3051.42$

Answer:

s:
(a) $\$151.42$
(b) $\$3051.42$