Question

A video streaming service subscriber pays $99. 99 per year for unlimited streaming. The subscriber pays for the service using a credit card with a 23. 99% APR. The subscriber

makes a payment of $15 for three months and then pays the balance off at the end of the fourth month. Determine how much additional interest the subscriber paid by paying the

balance off in four months instead paying it off during the grace period.

A. $7. 67

B. $2. 56

C. $6. 41

D. $1. 15

Answer 1

the answer is D. $1.15.

Explanation:

Given:

Annual subscription fee = $99.99

APR = 23.99%

Payment for three months = $15

To calculate the interest charged, we can use the formula for simple interest:

Interest = Principal × Rate × Time

Principal = Remaining balance after three months

Rate = APR

Time = Number of months (1 month)

The remaining balance after three months can be calculated by subtracting the payments made from the annual subscription fee:

Remaining balance = Annual subscription fee - Payment for three months

Remaining balance = $99.99 - $15 * 3

Remaining balance = $99.99 - $45

Remaining balance = $54.99

Now, we can calculate the interest charged for one month:

Interest = Remaining balance × (Rate / 12) × Time

Interest = $54.99 × (0.2399 / 12) × 1

Interest ≈ $1.094

Therefore, the additional interest paid by the subscriber for paying off the balance in four months instead of during the grace period is approximately $1.094.

The closest option from the given choices is:

D. $1.15

Answer 2

To calculate the additional interest paid, we first need to understand how interest is charged.

For a credit card, if the statement balance isn't paid in full by the due date, interest is typically calculated daily on the average daily balance for that billing cycle. The grace period is the time between the end of a billing cycle and the due date for that bill; during this time, no interest is charged if the bill is paid in full by the due date.

In this case, the subscriber pays off part of the balance in the first three months and then the rest at the end of the fourth month.

Let's calculate the interest:

First, convert the annual percentage rate (APR) to a daily rate:

23.99% per year = 23.99 / 365 = 0.0657534% per day

Month 1:

Beginning balance: $99.99

Payment: $15

Balance after payment: $99.99 - $15 = $84.99

Interest for the month: $84.99 * (0.0657534/100) * 30 = $1.67

Month 2:

Beginning balance: $84.99 + $1.67 = $86.66

Payment: $15

Balance after payment: $86.66 - $15 = $71.66

Interest for the month: $71.66 * (0.0657534/100) * 30 = $1.41

Month 3:

Beginning balance: $71.66 + $1.41 = $73.07

Payment: $15

Balance after payment: $73.07 - $15 = $58.07

Interest for the month: $58.07 * (0.0657534/100) * 30 = $1.14

Month 4:

Beginning balance: $58.07 + $1.14 = $59.21

Interest for the month: $59.21 * (0.0657534/100) * 30 = $1.16

Total Interest Paid: $1.67 + $1.41 + $1.14 + $1.16 = $5.38

If the subscriber had paid off the balance during the grace period, no interest would have been charged. Therefore, the additional interest paid is $5.38. However, this option isn't given among the provided choices. Please double-check the problem or options.