Hi Katie!
Great question! The trick here is recognizing that your minimum monthly payment covers only the interest, not any of the principal. That means we can calculate how much additional debt you can take on while keeping your monthly payment exactly the same.
Step 1: Calculate your current minimum monthly payment.
Your original credit card has:
- Outstanding balance: $25,000
- Annual percentage rate (APR): 15%
- Monthly interest rate: 15% ÷ 12 = 1.25%
Since you're only required to pay the interest each month:
Monthly Payment = $25,000 × (0.15 ÷ 12)
Monthly Payment = $312.50
This is the amount we want to keep unchanged.
Step 2: Determine how much you can borrow at the new interest rate.
Your new credit card has a lower APR of 12%, meaning its monthly interest rate is:
12% ÷ 12 = 1%
We want to find the total balance that would generate the same $312.50 monthly interest payment.
Monthly Payment = New Balance × Monthly Interest Rate
$312.50 = New Balance × 0.01
New Balance = $312.50 ÷ 0.01
New Balance = $31,250
Step 3: Calculate the additional amount you can borrow.
Remember, you already owe $25,000, so the $31,250 represents your total borrowing capacity at the new rate while maintaining the same monthly payment.
Additional Borrowing = $31,250 − $25,000
Final Answer: $6,250
Quick check:
Old card: $25,000 × 1.25% = $312.50/month
New card: $31,250 × 1% = $312.50/month
Both payments are identical!
Key takeaway: When your payments cover only interest, a lower interest rate allows you to carry a larger principal balance without increasing your monthly payment. However, keep in mind that your total debt would increase, even though your monthly payment stays the same.
Hope this helps!
Michael
