Question

Credit card a has an apr of 26,2% and an annual fee of 930, while eredit card d has an apr of 27.1% and no annual fee. all else being equal, at about what balance will the cards offer the same deal over the course of a year? (assume all interest is compounded monthly.)

a) $3,000
b) $4,500
c) $6,200
d) $8,000

Answer 1

To find the balance at which the two credit cards offer the same deal over the course of a year, set up an equation based on the interest and fees of each card. Simplify the equation and solve for 'b' to find the balance. At an approximate balance of $8,058, both Credit Card A and Credit Card D will offer the same deal over the course of a year.

Step-by-step explanation:

To find the balance at which the two credit cards offer the same deal over the course of a year, we can set up an equation based on the interest and fees of each card. Let's use the variable 'b' to represent the balance.

For Credit Card A: The APR of 26.2% compounded monthly would result in a monthly interest rate of (26.2/12)%. Additionally, the annual fee of $930 would be spread out over 12 months, so there would be a monthly fee of $930/12. The total cost per month would be (b * (26.2/12)%/100) + ($930/12).

For Credit Card D: The APR of 27.1% compounded monthly would result in a monthly interest rate of (27.1/12)%. Since there is no annual fee, the total cost per month would be (b * (27.1/12)%/100).

Setting up the equation: (b * (26.2/12)%/100) + ($930/12) = (b * (27.1/12)%/100)

Simplifying the equation and solving for 'b', we find that:

b = ($930/12) / (((27.1/12)%/100) - ((26.2/12)%/100))

Calculating the approximate value of 'b', we find that:

b ≈ $8,058