Question

Suppose that on January 1 you have a balance of $3800 on a credit card whose APR is 21%, 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? (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

A. $353.83

B. $4245.96

C. 10.5%

Explanation:

You want the monthly payments, the total paid, and the fraction of that payment that is interest on a credit card balance of $3800 with an APR of 21% that you pay off in a year.

A. Payment

The monthly payment can be found from the formula ...

A = P(r/12)/(1 -(1 +r/12)^(-12))

where P is the principal value of the loan, r is the APR, and the loan is paid in 12 payments.

A = $3800(0.21/12)/(1 -(1 +0.21/12)^-12) ≈ $353.83

The monthly payments will be $353.83.

B. Total paid

The total amount paid is the amount of 12 payments:

12($353.83) = $4245.96

You will have paid $4245.96 in the year.

C. Interest part

The amount of interest is ...

$4245.96 -3800 = $445.96

The fraction of the total that is interest is ...

$445.96/($4245 -3800) × 100% ≈ 10.5%

About 10.5% of the total payment is interest.

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