Final answer:
Mathematical analysis of credit card options involves comparing fixed and variable APRs, with the general advice being to choose the lowest fixed rate for predictable costs.
Step-by-step explanation:
The question falls under Mathematics, specifically in the area of personal finance related to credit card interest rates. Analyzing credit card options requires understanding the terms of each card. A fixed annual percentage rate (APR) means the interest rate is constant throughout the year, whereas a variable APR implies that the rate may fluctuate based on an index or market rates.
The average credit card interest rate as of 2021 was around 15%, with rates varying from 12% to 18%. Given the scenarios with fixed and variable rates of 17%, 15%, and 20%, it would be financially wise to choose the card with the lowest fixed rate if one plans to carry a balance, as this ensures predictable payments and potential cost savings. However, one must also consider other fees and the possibility of fluctuating rates with the variable interest option.