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Answer:
Therefore, you would save approximately $58.68 by paying off the balance on the 1st day of the billing cycle instead of the 30th day.
Step-by-step explanation:
To calculate the amount of money you would save by paying off the balance on the 1st day of the billing cycle instead of the 30th day, we need to understand how interest accrues on a daily basis.
1. **Daily interest rate calculation:**
- The APR (Annual Percentage Rate) is 22.31%.
- The daily interest rate is calculated by dividing the APR by 365 (the number of days in a year).
\[
\text{Daily interest rate} = \frac{22.31\%}{365} = \frac{0.2231}{365} \approx 0.0006112 \text{ (or 0.06112% per day)}
\]
2. **Interest accrued over 30 days:**
- The interest accrued daily on the outstanding balance of $3,200 is calculated as:
\[
\text{Daily interest} = 3200 \times 0.0006112 \approx 1.956 \text{ USD}
\]
- Over 30 days, the total interest accrued is:
\[
\text{Interest for 30 days} = 1.956 \times 30 \approx 58.68 \text{ USD}
\]
3. **Interest if paid off on the 1st day:**
- If you pay off the balance on the 1st day, no interest would accrue.
4. **Savings calculation:**
- The amount saved by paying off the balance on the 1st day instead of the 30th day is the total interest accrued over 30 days.
\[
\text{Savings} = 58.68 \text{ USD}
\]
Therefore, you would save approximately $58.68 by paying off the balance on the 1st day of the billing cycle instead of the 30th day.