To determine the interest charge on Gordon's average daily balance for one billing cycle, we need to follow a step-by-step process. Here are the steps:
1. Determine the daily interest rate:
The APR (Annual Percentage Rate) is given as 12%, which is expressed as 0.12 in decimal form. To convert this annual rate to a daily rate, we divide by the number of days in a year.
[tex]\[
\text{Daily interest rate} = \frac{\text{APR}}{\text{Days in a year}} = \frac{0.12}{365} = 0.00032876712328767124
\][/tex]
2. Calculate the interest charge for one billing cycle:
We now use this daily rate to determine the interest charge over the 30-day billing cycle. The formula to calculate the interest charge is:
[tex]\[
\text{Interest charge} = \text{Daily interest rate} \times \text{Average daily balance} \times \text{Billing cycle days}
\][/tex]
Substituting the given values:
[tex]\[
\text{Interest charge} = 0.00032876712328767124 \times 1200 \times 30
\][/tex]
Performing the calculation:
[tex]\[
\text{Interest charge} = 11.835616438356164
\][/tex]
Therefore, the calculated interest charge on Gordon's average daily balance for one billing cycle is approximately \[tex]$11.84.
In conclusion:
- The daily interest rate is approximately 0.00032876712328767124.
- The interest charge for the billing cycle is approximately \$[/tex]11.83.
