Credit card A has an APR of 19.3% and an annual fee of $84, while credit card B has an APR of 24.6% and no annual fee. All else being equal, which of these equations can be used to solve for the principal P for which the cards offer the same deal over the course of a year? (Assume all interest is compounded monthly.)

The equations are missing but we can solve the problem from the given information

The equation    can be used to solve for the principal P for which the cards offer the same deal over the course of a year

Step-by-step explanation:

The formula of the compounded interest is , where

Card A:

∵ Credit card A has an APR of 19.3% and an annual fee of $84

∴ r = 19.3% = 19.3 ÷ 100 = 0.193

∴ Annual fee = 84

∵ Interest is compounded monthly for a year

∴ n = 12 and t = 1

- Substitute the values of r, n and t in the formula above

∴

- Add the value of the annual fee

∴

Card B:

∵ Credit card B has an APR of 24.6% and no annual fee

∴ r = 24.6% = 24.6 ÷ 100 = 0.246

∴ Annual fee = 0

∵ Interest is compounded monthly for a year

∴ n = 12 and t = 1

- Substitute the values of r, n and t in the formula above

∴

∴

- Equate The equations of cards A and B

∴

The equation    can be used to solve for the principal P for which the cards offer the same deal over the course of a year

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