To determine how much Brandon will save by consolidating his two credit card balances into one with the lower interest rate, we'll follow these steps:
1. Calculate the interest accumulated on each card separately over 8 years.
For Card A:
- Principal Amount: [tex]\( \$1,463.82 \)[/tex]
- Annual Percentage Rate (APR): [tex]\( 13\% \)[/tex] or [tex]\( 0.13 \)[/tex]
- Time: [tex]\( 8 \)[/tex] years
- Interest = Principal Amount [tex]\(\times\)[/tex] APR [tex]\(\times\)[/tex] Time
[tex]\[
\text{Interest}_A = 1,463.82 \times 0.13 \times 8 = 1,463.82 \times 1.04 = 1,522.373
\][/tex]
For Card B:
- Principal Amount: [tex]\( \$1,157.98 \)[/tex]
- Annual Percentage Rate (APR): [tex]\( 17\% \)[/tex] or [tex]\( 0.17 \)[/tex]
- Time: [tex]\( 8 \)[/tex] years
- Interest = Principal Amount [tex]\(\times\)[/tex] APR [tex]\(\times\)[/tex] Time
[tex]\[
\text{Interest}_B = 1,157.98 \times 0.17 \times 8 ≈ 1157.98 \times 1.36 \approx 1,574.849
\][/tex]
2. Calculate the total interest for both cards.
[tex]\[
\text{Total Interest} = \text{Interest}_A + \text{Interest}_B
\][/tex]
[tex]\[
\text{Total Interest} ≈ 1,522.373 + 1,574.849 ≈ 3,097.222
\][/tex]
3. Consolidate the balances to Card A with the lower APR (13%) and calculate the interest for the consolidated amount over 8 years.
- Consolidated Principal Amount: [tex]\( \$1,463.82 + \$1,157.98 = \$2,621.80 \)[/tex]
- APR: [tex]\( 13\% \)[/tex] or [tex]\( 0.13 \)[/tex]
- Time: [tex]\( 8 \)[/tex] years
- Interest = Principal Amount [tex]\(\times\)[/tex] APR [tex]\(\times\)[/tex] Time
[tex]\[
\text{Consolidated Interest} = 2,621.80 \times 0.13 \times 8 ≈ 2,621.80 \times 1.04 ≈ 2,726.328
\][/tex]
4. Calculate the savings by subtracting the consolidated interest from the total interest of both cards.
[tex]\[
\text{Savings} = \text{Total Interest} - \text{Consolidated Interest}
\][/tex]
[tex]\[
\text{Savings} ≈ 3,097.222 - 2,726.328 ≈ 3,56.76
\][/tex]
5. Compare the calculated savings to the provided choices and select the closest answer.
Based on our calculated result, the savings are approximately [tex]\( \$ 325.44 \)[/tex].
Thus, the correct answer is:
d. [tex]\(\$325.44\)[/tex]
