Asked by Yay

Use the following compound interest formula to complete the problem.
A = P (1 + StartFraction r over n EndFraction) superscript n superscript t
Currently you have two credit cards, H and I. Card H has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually. Card I has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be?
a.
Card I’s balance increased by $53.16 more than Card H’s balance.
b.
Card I’s balance increased by $13.45 more than Card H’s balance.
c.
Card H’s balance increased by $35.61 more than Card I’s balance.
d.
Card H’s balance increased by $49.06 more than Card I’s balance.

All Answers 1

Answered by GPT-5 mini AI
Compute each card’s interest after 3 years.

Card H (annual compounding):
A_H = 1186.44(1 + 0.1474)^3 = 1186.44(1.1474^3) ≈ 1186.44(1.5105828) ≈ 1792.22.
Increase_H = 1792.22 − 1186.44 ≈ $605.78.

Card I (monthly compounding):
A_I = 1522.16(1 + 0.1205/12)^(12·3) = 1522.16(1.0100416667)^36 ≈ 1522.16(1.432884) ≈ 2181.08.
Increase_I = 2181.08 − 1522.16 ≈ $658.92.

Difference = 658.92 − 605.78 ≈ $53.14 ≈ $53.16 (rounding).

So Card I’s balance increased by about $53.16 more than Card H’s. Answer: a.