Question

A grocery delivery service subscriber pays $135.99 per year for unlimited deliveries. The subscriber pays for the service using a credit card with a 16.99% APR. If the balance is paid off after one month of interest charges, how much more will have been paid instead of using cash?

$19.30
$23.10
$1.93
$3.88

Answer 1

C) $1.93

Explanation:

To calculate the additional amount paid for using the credit card instead of cash, we need to consider the interest charges incurred over one month.

The annual interest rate is 16.99%.

Calculate the monthly interest rate by dividing the annual interest rate by 12 (number of months in a year):

`\textsf{Monthly interest rate} = (16.99\%)/(12) =1.4158333...\%=0.014158333...`

Now we can calculate the interest charged on the annual subscription fee for one month:

`\begin{aligned}\textsf{Interest charged}& = \textsf{Annual subscription fee} * \textsf{Monthly interest rate}\\\\&=\$135.99 * 0.014158333...\\\\&=1.92539175\\\\&= \$1.93\; \textsf{(nearest cent)}\end{aligned}`

Therefore, the additional amount paid instead of using cash is approximately $1.93.

Answer 2

$1.93

Explanation:

The first step is to find out how much interest will accrue in one month on the annual fee of $135.99.

`\rm\implies{Interest = (APR * Balance)/(12)}`

Substitute the given values into the formula:

`\begin{aligned}\rm\implies Interest& =\rm (16.99 * 135.99)/(12)\\&=\rm(23.104701)/(12)\\& \approx \boxed{\rm{\$1.93}}\end{aligned}`

`\therefore` The subscriber will have paid an additional $1.93 in interest charges by using their credit card instead of paying in cash.