Question

Your parents purchase a computer for $1,257.00 plus 6% sales tax. They decide to finance it through the store’s 0% program for 6 months. The terms state that they pay nothing until the 6 months are over. When they receive the bill, they forget to pay it and are assessed a late fee of $45.00 plus the interest accrued to that point at a 16.75% APR. What is the accrued interest after 6 months?
(1 point)
Responses

$109.02
$109.02

$115.56
$115.56

$223.18
$223.18

$111.59

Answer 1

To calculate the accrued interest after 6 months, we first need to determine the total amount financed, which includes the original purchase price and the sales tax.

1. **Calculate the sales tax:**
\[
\text{Sales Tax} = 1,257.00 \times 0.06 = 75.42
\]

2. **Calculate the total amount financed:**
\[
\text{Total Amount} = 1,257.00 + 75.42 = 1,332.42
\]

3. **Calculate the annual interest rate in decimal form:**
\[
\text{APR} = 16.75\% = 0.1675
\]

4. **Calculate the monthly interest rate:**
\[
\text{Monthly Interest Rate} = \frac{0.1675}{12} \approx 0.01395833
\]

5. **Calculate the accrued interest over 6 months:**
\[
\text{Accrued Interest} = \text{Total Amount} \times \text{Monthly Interest Rate} \times 6
\]
\[
\text{Accrued Interest} = 1,332.42 \times 0.01395833 \times 6
\]
\[
\text{Accrued Interest} \approx 1,332.42 \times 0.083750
\]
\[
\text{Accrued Interest} \approx 111.65
\]

Since $111.65 is not one of the options, let’s round this properly:

Given that interest is calculated, it could slightly differ, but it’s possible the closest match is required.

The closest choice provided to our calculation is **$111.59**.

Thus, the answer is:
**$111.59**