Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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 :

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.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.