Credit Card Decision

Algebra Level pending

One credit card offers 4 % 4 \% cash back on purchases, with an annual fee of 95 95 dollars. Another card offers 3 % 3 \% cash back on purchases, with no annual fee.

On average, how much do you have to purchase each day for the card with the annual fee to be the better pick?

Details and Assumptions:
1) Give your answer in dollars, rounded to the nearest dollar
2) Assume that there are 365 365 days in a year


The answer is 26.

Steven Chase by Steven Chase , 37, USA

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1 solution

If the daily purchase be worth x x dollars, then ( 97 100 − 96 100 ) × 365 x < 95 \left (\dfrac {97}{100}-\dfrac {96}{100}\right ) \times 365x<95

⟹ x < 9500 365 \implies x<\dfrac{9500}{365} .

Hence the required answer is 26 \boxed {26} dollars.

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