Question

Suppose that on January 1 you have a balance of $10,000 on each of rthe following credit cards, which you want to pay off in the given amount of time. Assume that you make no additional charges on 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 the total payment found in part (b) is for interest? 30) The credit card APR is 20% and you want to pay off the balance in 2 years 32) The credit card APRI is 22% and you want to pay off the balance in 1 year

Answer 1

a) For the credit card with a 20% APR and a 2-year payoff period, the monthly payment is approximately $510.34. For the credit card with a 22% APR and a 1-year payoff period, the monthly payment is approximately $921.12. b) The total amount paid since January 1 will be $12,248.16 for the 20% APR card and $11,053.44 for the 22% APR card. c) The interest percentage for the 20% APR card is approximately 22.48%, and for the 22% APR card, it is approximately 10%.

Step-by-step explanation:

a) To calculate the monthly payments, we can use the formula for monthly payments on an amortizing loan:
`\[PMT = (P \cdot r \cdot (1 + r)^n)/((1 + r)^n - 1)\]`, where PMT is the monthly payment, P is the principal (initial balance), r is the monthly interest rate, and n is the total number of payments (months). For the 20% APR card with a 2-year payoff, the monthly payment is approximately $510.34. For the 22% APR card with a 1-year payoff, the monthly payment is approximately $921.12.

b) The total amount paid since January 1 can be calculated by multiplying the monthly payment by the total number of payments. For the 20% APR card, it is $510.34 * 24 = $12,248.16, and for the 22% APR card, it is $921.12 * 12 = $11,053.44.

c) The interest percentage is calculated by subtracting the initial balance from the total amount paid and then dividing by the initial balance. For the 20% APR card, it is approximately 22.48%, and for the 22% APR card, it is approximately 10%. These percentages represent the portion of the total payment that goes towards interest.

In summary, these calculations provide a clear understanding of the monthly payments, total amount paid, and the percentage allocated to interest for two credit cards with different APRs and payoff periods.