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

The correct option is a. Card Q’s balance increased by $7.22 more than Card P’s balance.

To determine which card's balance will have increased more after four years, we can use the compound interest formula:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

Where:

-
`\( A \)` is the total amount after time
`\( t \)`,

-
`\( P \)` is the principal amount (initial balance),

-
`\( r \)` is the annual interest rate (in decimal form),

-
`\( n \)` is the number of times interest is compounded per year,

-
`\( t \)` is the time in years.

For Card P:

`\[ A_P = 726.19 \left(1 + (0.1019)/(2)\right)^(2 * 4) \]`

For Card Q:

`\[ A_Q = 855.20 \left(1 + (0.0863)/(12)\right)^(12 * 4) \]`

Calculate both
`\( A_P \)` and
`\( A_Q \)` and find the difference
`\( \Delta A = A_Q - A_P \).`

After calculations, the correct answer is:

a. Card Q's balance increased by $7.22 more than Card P's balance.