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Sure, let's walk through a concrete example illustrating how high interest rates can trap someone in credit card debt.

Example Scenario:
Imagine Sarah has a credit card with a 20% annual percentage rate (APR). She has a balance of $5,000 on her card, which she is unable to pay off in full immediately. Instead, she makes the minimum payment each month.

Calculations:
1. Interest Calculation:
   - Monthly interest rate: \( \frac{20\%}{12} = 1.67\% \)

2. Minimum Payment:
   - Assuming her minimum payment is 2% of her balance or $25, whichever is greater.
   - For the first month: \( 2\% \times $5,000 = $100 \) (this exceeds $25, so she pays $100).

3. First Month:
   - Interest added to the balance: \( 1.67\% \times $5,000 = $83.50 \).
   - New balance after interest: \( $5,000 + $83.50 = $5,083.50 \).
   - Balance after minimum payment: \( $5,083.50 - $100 = $4,983.50 \).

4. Subsequent Months:
   - For the second month, the process repeats.
   - New interest: \( 1.67\% \times $4,983.50 \approx $83.26 \).
   - New balance: \( $4,983.50 + $83.26 \approx $5,066.76 \).
   - Minimum payment (2% of $5,066.76): \( $101.34 \).
   - Balance after minimum payment: \( $5,066.76 - $101.34 \approx $4,965.42 \).

As the months progress, even though Sarah is making minimum payments, the interest continues to accumulate. Here's what happens over a year if she continues to make minimum payments:

End of Year:
- Sarah will have paid approximately $1,200 in minimum payments (12 months × $100).
- However, due to the high interest rate, a large portion of her payments goes toward interest, not the principal balance.
- After one year, her balance would be only slightly reduced, and she would have paid a significant amount in interest.

Total Interest Paid:
- Over a year, the interest added to her balance is substantial. If Sarah's balance decreases very slowly, she could end up paying a significant amount in interest without making much progress on the principal.

This example demonstrates how high interest rates can trap someone in debt. The interest charges add up quickly, and making only the minimum payments means that most of the payment goes toward interest, not reducing the principal balance. As a result, the debt persists, and the person may find it challenging to pay off the balance.