$$ \frac{1}{365} $$ of a year. Answer each part below. not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refor to the list of financial formulas. $$ \$ 7900 $$ from a credit union for 124 days. The credit union charges simple interest at an annual rate of $$ 10 \% $$ for this loan. Assume each day (a) Find the interest that will be owed after 124 days. (b) Assuming the print shop doesn't make any payments, find the amount owed after 124 days. $$ \$ \square $$

Question

UpStudy AI · Accepted Answer

Let's solve each part step by step using the simple interest formula:

$$
I = P \times r \times t
$$

Where:
- $$ I $$ = Interest
- $$ P $$ = Principal amount (\$7,900)
- $$ r $$ = Annual interest rate (10% or 0.10)
- $$ t $$ = Time in years

Given that each day is $$ \frac{1}{365} $$ of a year, for 124 days:

$$
t = \frac{124}{365}
$$

### Part (a): Calculate the Interest Owed After 124 Days

Plugging the values into the simple interest formula:

$$
I = 7900 \times 0.10 \times \frac{124}{365}
$$

$$
I = 790 \times \frac{124}{365}
$$

$$
I = \frac{97,960}{365} \approx 268.3836
$$

Rounding to the nearest cent:

$$
I \approx \$268.38
$$

### Part (b): Calculate the Total Amount Owed After 124 Days

The total amount owed is the sum of the principal and the interest:

$$
\text{Total Amount} = P + I
$$

$$
\text{Total Amount} = 7900 + 268.38 = 8168.38
$$

Rounding to the nearest cent:

$$
\text{Total Amount} = \$8,168.38
$$

### Final Answers

**(a)** The interest owed after 124 days is **\$268.38**.

**(b)** The total amount owed after 124 days is **\$8,168.38**.
**(a)** The interest owed after 124 days is **\$268.38**. **(b)** The total amount owed after 124 days is **\$8,168.38**.

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