Question

11. You have credit card debt of $25,000 that has an APR (monthly compounding) of 15%. Each month you pay the minimum monthly payment only. You are required to pay only the outstanding interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 12%. After considering all your alternatives, you decide to switch cards, roll over the outstanding balance on the old card into the new card, and borrow additional money as well. How much can you borrow today on the new card without changing the minimum monthly payment you will be required to pay? Assumption: (i) treat the interest payments as perpetuity; (ii) your current monthly payment is the interest that accrues

Answer 1

The student can borrow an additional $6,250 on the new credit card with a 12% APR, enabling them to maintain the same monthly payment of $312.50, originally calculated based on the old credit card's 15% APR.

Step-by-step explanation:

The student is facing a common financial dilemma involving credit card debt and is considering switching to a card with a lower annual percentage rate (APR). Given their current situation of having a $25,000 debt with a 15% APR (compounded monthly), the minimum payment each month would be the interest accrued. In the scenario provided, the student is evaluating an offer for a new credit card with a 12% APR and is contemplating how much additional money they can borrow without changing their current minimum monthly payment.

To solve this, we need to calculate the current monthly interest payment with the old APR and see how this would translate to the new APR. A perpetuity payment formula can be used, where the minimum monthly payment (current interest payment) is equal to the principal (amount borrowed) multiplied by the monthly interest rate. By comparing the monthly interest payments at 15% and 12% APR, we can determine the maximum amount the student could borrow on the new card.

For the current card at 15% APR, the monthly interest rate is 15% / 12 months = 1.25% per month. So, the current monthly interest payment is $25,000 x 1.25% = $312.50. For the new card with a 12% APR, the monthly interest rate is 12% / 12 months = 1% per month. To maintain the same monthly payment of $312.50, the new balance the student could have on the new card without changing the minimum monthly payment would be calculated by $312.50 / 1% = $31,250. Therefore, the student can borrow an additional $6,250 ($31,250 - $25,000) on the new card while keeping the same monthly interest payment.

Answer 2

We can borrow an additional 6,250 dollars

Step-by-step explanation:

credit card rate:

old one: 0.15 / 12 = 0.0125 percent per month

new one: 0.12 / 12 = 0.01

interest forthe old car:

25,000 x 0.0125 = 312,5

now we convert this payment in a perpetuity with a rate of 0.01

312,5 / 0.01 = 31.250‬

maximun balance 31,250 current balance 25,000

available for loan 6,250 (31,250 - 25,000)