Question

Use the following compound interest formula to complete the problem.
A = P (1 + StartFraction r over n EndFraction) superscript n superscript t
Sandra has two credit cards, P and Q. Card P has a balance of $726.19 and an interest rate of 10.19%, compounded semiannually. Card Q has a balance of $855.20 and an interest rate of 8.63%, compounded monthly. Assuming that Sandra makes no purchases and no payments with either card, after four years, which card’s balance will have increased by more, and how much greater will that increase be?
a.
Card Q’s balance increased by $7.22 more than Card P’s balance.
b.
Card Q’s balance increased by $6.69 more than Card P’s balance.
c.
Card P’s balance increased by $3.43 more than Card Q’s balance.
d.
Card P’s balance increased by $0.80 more than Card Q’s balance.

Answer 1

Compute each new balance after 4 years.

Card P:
A_P = 726.19(1 + 0.1019/2)^{2·4} = 726.19(1.05095)^8 ≈ 1080.69
Increase_P ≈ 1080.69 − 726.19 = $354.50

Card Q:
A_Q = 855.20(1 + 0.0863/12)^{12·4} = 855.20(1.007191667)^{48} ≈ 1206.32
Increase_Q ≈ 1206.32 − 855.20 = $351.12

Difference ≈ 354.50 − 351.12 = $3.38 (Card P increased more).

The closest answer choice is c: Card P’s balance increased by $3.43 more than Card Q’s.