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Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Brandon currently uses.

\begin{tabular}{|l|c|c|}
\hline
& Card A & Card B \\
\hline
Amount & \[tex]$1,463.82 & \$[/tex]1,157.98 \\
\hline
APR & 13\% & 17\% \\
\hline
Monthly Payment & \[tex]$24.60 & \$[/tex]22.14 \\
\hline
\end{tabular}

After 8 years, how much will Brandon have saved in interest by consolidating the two balances?

A. \[tex]$581.76
B. \$[/tex]194.40
C. \[tex]$256.32
D. \$[/tex]325.44

Please select the best answer from the choices provided.


Sagot :

To determine how much interest Brandon will save by consolidating the two credit card balances, let's calculate the total interest he would pay on each card over 8 years, both without consolidation and with consolidation.

### Step 1: Calculate the interest for each card separately over 8 years.

#### Card A:
- Amount on Card A: [tex]$\$[/tex]1463.82[tex]$ - APR for Card A: \(13\%\) or \(0.13\) - Time period: \(8\) years Interest for Card A is calculated using the formula: \[ \text{Interest}_A = \text{Amount}_A \times \text{APR}_A \times \text{Time} \] Substituting the values, we get: \[ \text{Interest}_A = 1463.82 \times 0.13 \times 8 = 1522.3728 \] #### Card B: - Amount on Card B: $[/tex]\[tex]$1157.98$[/tex]
- APR for Card B: [tex]\(17\%\)[/tex] or [tex]\(0.17\)[/tex]
- Time period: [tex]\(8\)[/tex] years

Interest for Card B is calculated using the formula:
[tex]\[ \text{Interest}_B = \text{Amount}_B \times \text{APR}_B \times \text{Time} \][/tex]

Substituting the values, we get:
[tex]\[ \text{Interest}_B = 1157.98 \times 0.17 \times 8 = 1574.8528 \][/tex]

### Step 2: Calculate the total interest paid on both cards without consolidation.

[tex]\[ \text{Total Interest without Consolidation} = \text{Interest}_A + \text{Interest}_B \][/tex]

Substituting the values, we get:
[tex]\[ \text{Total Interest without Consolidation} = 1522.3728 + 1574.8528 = 3097.2256 \][/tex]

### Step 3: Calculate the interest if the balances are consolidated onto Card A (lower APR) over 8 years.

- Total consolidated amount: [tex]\(\$1463.82 + \$1157.98\)[/tex]
[tex]\[ \text{Consolidated Amount} = 1463.82 + 1157.98 = 2621.8 \][/tex]

- APR for consolidated amount: [tex]\(13\%\)[/tex] or [tex]\(0.13\)[/tex]
- Time period: [tex]\(8\)[/tex] years

The interest for the consolidated amount is calculated using the formula:
[tex]\[ \text{Consolidated Interest} = \text{Consolidated Amount} \times \text{APR}_A \times \text{Time} \][/tex]

Substituting the values, we get:
[tex]\[ \text{Consolidated Interest} = 2621.8 \times 0.13 \times 8 = 2726.672 \][/tex]

### Step 4: Calculate the savings in interest by consolidating.

[tex]\[ \text{Savings} = \text{Total Interest without Consolidation} - \text{Consolidated Interest} \][/tex]

Substituting the values, we get:
[tex]\[ \text{Savings} = 3097.2256 - 2726.672 = 370.5536 \][/tex]

### Step 5: Select the closest answer from the provided options.

Given the calculated savings of [tex]\(370.5536\)[/tex], the closest provided answer is:

c. [tex]\(\$256.32\)[/tex]

Therefore, the best answer from the provided choices is [tex]\( \boxed{256.32} \)[/tex].