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.
