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Marcia has two credit cards and wants to consolidate the balances into one card with the lower interest rate. The table below shows information about the two credit cards:

| | Card A | Card B |
|------------|----------|----------|
| Amount | [tex]$1,389.47| $[/tex]1,065.32|
| APR | 16% | 12% |
| Monthly Payment | [tex]$39.38 | $[/tex]28.05 |

After 4 years, approximately how much will Marcia save in interest by consolidating the two balances?

a. [tex]$1,890.24
b. $[/tex]133.92
c. [tex]$543.84
d. $[/tex]1,346.40

Sagot :

GinnyAnsweridn
To determine how much Marcia will save in interest by consolidating the two balances, let's follow a step-by-step process to calculate the interest for both individual cards and the consolidated balance.

### Step 1: Calculate the interest on Card A
- Balance of Card A: \[tex]$1,389.47 - APR for Card A: 16% (0.16 as a decimal) - Number of years: 4 We use the formula for simple interest: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] So, the interest on Card A: \[ \text{Interest}_A = \$[/tex]1,389.47 \times 0.16 \times 4 \]
[tex]\[ \text{Interest}_A = \$889.2608 \][/tex]

### Step 2: Calculate the interest on Card B
- Balance of Card B: \[tex]$1,065.32 - APR for Card B: 12% (0.12 as a decimal) - Number of years: 4 Again, using the simple interest formula: \[ \text{Interest}_B = \$[/tex]1,065.32 \times 0.12 \times 4 \]
[tex]\[ \text{Interest}_B = \$511.3536 \][/tex]

### Step 3: Calculate the consolidated interest
Let's assume Marcia consolidates the balance onto Card B, which has the lower APR.

- Total consolidated balance: \[tex]$1,389.47 + \$[/tex]1,065.32 = \[tex]$2,454.79 - APR for consolidated balance: 12% (0.12 as a decimal) - Number of years: 4 Using the simple interest formula for the consolidated balance: \[ \text{Consolidated Interest} = \$[/tex]2,454.79 \times 0.12 \times 4 \]
[tex]\[ \text{Consolidated Interest} = \$1,178.2992 \][/tex]

### Step 4: Calculate the interest saved by consolidating
We need to find the difference between the total interest paid individually and the consolidated interest.

- Total individual interest:
[tex]\[ \text{Interest}_A + \text{Interest}_B = \$889.2608 + \$511.3536 \][/tex]
[tex]\[ \text{Total Individual Interest} = \$1,400.6144 \][/tex]

- Interest saved by consolidating:
[tex]\[ \text{Interest Saved} = \text{Total Individual Interest} - \text{Consolidated Interest} \][/tex]
[tex]\[ \text{Interest Saved} = \$1,400.6144 - \$1,178.2992 \][/tex]
[tex]\[ \text{Interest Saved} = \$222.3152 \][/tex]

Thus, by consolidating the two balances, Marcia will save approximately \[tex]$222.32 in interest. ### Answer So, the correct answer is not listed among the provided options. According to our calculation, the interest saved is approximately \$[/tex]222.32.
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