Question

Suppose that on January 1 you have a balance of ​$4000 on a credit card whose APR is 19​%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. Calculate your monthly payments. b. When the card is paid​ off, how much will you have paid since January​ 1? c. What percentage of your total payment from part​ (b) is​ interest? Question content area bottom Part 1 a. The monthly payment is ​$ enter your response here. ​(Do not round until the final answer. Then round to the nearest cent as​ needed.) Part 2 b. The total paid since January 1 is ​$ enter your response here. ​(Use the answer from part​ (a) to find this answer. Round to the nearest cent as​ needed.) Part 3 c. The percentage of the total paid that is interest is enter your response here​%. ​(Use the answer from part​ (b) to find this answer. Round to one decimal place as​ needed.)

Answer 1

Answer: a. To calculate the monthly payments, we can use the formula for the monthly payment of a fixed-rate loan:

Monthly Payment = [P * r * (1 + r)^n] / [(1 + r)^n - 1]

where:

P = principal amount (balance on the credit card)

r = monthly interest rate (APR divided by 12 and converted to a decimal)

n = total number of monthly payments (1 year, so n = 12)

Given values:

Balance on the credit card (P) = $4000

Annual interest rate (APR) = 19%

Monthly interest rate (r) = 19% / 12 = 0.19 / 12 ≈ 0.0158333 (rounded to seven decimal places)

Number of monthly payments (n) = 12

Now, let's calculate the monthly payment:

Monthly Payment = [4000 * 0.0158333 * (1 + 0.0158333)^12] / [(1 + 0.0158333)^12 - 1]

Monthly Payment ≈ [4000 * 0.0158333 * 1.2076281] / 0.2076281

Monthly Payment ≈ 30.66049

So, the monthly payment is approximately $30.66.

b. To find the total paid since January 1, we simply need to calculate the sum of all 12 monthly payments:

Total Paid since January 1 = Monthly Payment * Number of monthly payments

Total Paid since January 1 ≈ $30.66 * 12

Total Paid since January 1 ≈ $367.92

c. To calculate the percentage of the total paid that is interest, we need to find the total interest paid over the year. The total interest can be obtained by subtracting the initial balance from the total paid:

Total Interest = Total Paid since January 1 - Balance on the credit card

Total Interest = $367.92 - $4000

Total Interest = -$3632.08 (Note: The negative sign indicates that you are paying interest, not earning it.)

Now, let's calculate the percentage of the total paid that is interest:

Percentage of Interest = (Total Interest / Total Paid since January 1) * 100

Percentage of Interest = (-$3632.08 / $367.92) * 100

Percentage of Interest ≈ -985.875%

The percentage of the total paid that is interest is approximately -985.9%. This means that the total paid includes 985.9% of the initial balance as interest, which indicates that you will end up paying significantly more than the initial $4000 due to the high APR.