To calculate the interest savings in the first month by improving your credit score to "good" with a purchase of $1,500, we will compare the interest for both the "average" and "good" credit scenarios.
- Interest Rate for Good Credit: 5.00%
- Interest Rate for Average Credit: 5.85%
Now, let’s calculate the interest for both scenarios for the first month using the formula:
\[ \text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right) \]
Step 1: Calculate the First Month Interest for Good Credit
\[ \text{Interest (Good)} = 1500 \times \left(\frac{5.00%}{12}\right) \] \[ \text{Interest (Good)} = 1500 \times \left(\frac{0.05}{12}\right) \] \[ \text{Interest (Good)} = 1500 \times 0.0041667 \approx 6.25 \]
Step 2: Calculate the First Month Interest for Average Credit
\[ \text{Interest (Average)} = 1500 \times \left(\frac{5.85%}{12}\right) \] \[ \text{Interest (Average)} = 1500 \times \left(\frac{0.0585}{12}\right) \] \[ \text{Interest (Average)} = 1500 \times 0.004875 \approx 7.31 \]
Step 3: Calculate the Interest Savings
\[ \text{Interest Savings} = \text{Interest (Average)} - \text{Interest (Good)} \] \[ \text{Interest Savings} = 7.31 - 6.25 \approx 1.06 \]
Thus, if you improved your credit score to "good" and paid $1,500 on your purchase, you could save approximately $1.06 in interest in the first month.