To calculate the interest accrued on the credit card balance and the interest earned in a savings account, we can follow these steps:
Step 1: Calculate the interest accrued on the credit card
The formula to calculate the interest accrued for one month for a credit card is:
\[ \text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right) \]
- Principal: $976.34
- APR: 10.75% or 0.1075 as a decimal
Now substituting the values:
\[ \text{Interest}_{\text{credit card}} = 976.34 \times \left(\frac{0.1075}{12}\right) \]
Calculating:
\[ \text{Interest}_{\text{credit card}} = 976.34 \times 0.00895833 \approx 8.75 \]
Step 2: Calculate the interest earned in the savings account
The formula for the interest earned in a savings account for one month is similar:
\[ \text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right) \]
- Principal: $100.00
- APR: 2.75% or 0.0275 as a decimal
Now substituting the values:
\[ \text{Interest}_{\text{savings}} = 100.00 \times \left(\frac{0.0275}{12}\right) \]
Calculating:
\[ \text{Interest}_{\text{savings}} = 100.00 \times 0.00229167 \approx 0.23 \]
Step 3: Calculate the difference between the interest accrued and the interest earned
Now let's find the difference between the two amounts:
\[ \text{Difference} = \text{Interest}{\text{credit card}} - \text{Interest}{\text{savings}} \]
Substituting in the calculated values:
\[ \text{Difference} = 8.75 - 0.23 \approx 8.52 \]
Conclusion
The difference between the interest accrued by the credit card and what $100.00 would earn in a savings account over the span of one month is approximately $8.52.