Question

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

First, convert interest to the effective annual interest rate using this formula:

(1 + i/m)^m - 1, where m = 2 for semiannual and m = 12 for monthly. Then, use this formula to find the future worth:

F = P(1+i)^n, where P is $726.19 and $855.20, respectively, for Card P and Q. n is equal to 4.

Card P: F = 1080.704
Card Q: F = 1206.284

Then, find the amount decrease by subtracting F - P.

Card P: F - P = $354.514
Card Q: F - P = $351.084

The difference between the two is $3.43. Thus, the answer is C.

Answer 2

the correct answer is C. Card P’s balance increased by $3.43 more than Card Q’s balance.