Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's solve this problem step-by-step to find out which expression calculates the interest Joan was charged for the billing cycle.
1. Calculate the Average Daily Balance:
- Joan had a balance of \[tex]$6390 for the first 3 days. - She had a balance of \$[/tex]0 for the remaining 27 days of the 30-day billing cycle.
The average daily balance is calculated as:
[tex]\[ \text{Average Daily Balance} = \frac{(3 \text{ days} \times \$6390) + (27 \text{ days} \times \$0)}{30 \text{ days}} \][/tex]
Simplifying further:
[tex]\[ \text{Average Daily Balance} = \frac{(3 \times 6390) + (27 \times 0)}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{19170 + 0}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{19170}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = 639 \][/tex]
2. Convert APR to Daily Percentage Rate:
- The Annual Percentage Rate (APR) is 17%, which is equivalent to 0.17 as a decimal.
- The daily percentage rate is calculated by dividing the APR by the number of days in a year (365 days):
[tex]\[ \text{Daily Interest Rate} = \frac{0.17}{365} \][/tex]
This simplifies to:
[tex]\[ \text{Daily Interest Rate} \approx 0.0004657534 \][/tex]
3. Calculate the Interest Charged:
- Using the previous balance method, the interest charged can be calculated using the formula:
[tex]\[ \text{Interest} = \text{Daily Interest Rate} \times \text{Number of Days in Billing Cycle} \times \text{Average Daily Balance} \][/tex]
Plugging in the values from our calculations:
[tex]\[ \text{Interest} = 0.0004657534 \times 30 \times 639 \][/tex]
Simplifying further:
[tex]\[ \text{Interest} = 0.0004657534 \times 19170 \][/tex]
[tex]\[ \text{Interest} \approx 8.928493 \][/tex]
4. Choose the Correct Expression:
We look for the expression that matches the calculation steps we have taken. The correct expression is:
A. [tex]\(\left(\frac{0.17}{365} \cdot 30\right)\left(\frac{3 \cdot \$ 6390+27 \cdot \$ 0}{30}\right)\)[/tex]
This matches perfectly with our step-by-step solution. Therefore, the correct expression to calculate the amount Joan was charged in interest for the billing cycle is:
Option A: [tex]\(\left(\frac{0.17}{365} \cdot 30\right)\left(\frac{3 \cdot \$ 6390+27 \cdot \$ 0}{30}\right)\)[/tex]
1. Calculate the Average Daily Balance:
- Joan had a balance of \[tex]$6390 for the first 3 days. - She had a balance of \$[/tex]0 for the remaining 27 days of the 30-day billing cycle.
The average daily balance is calculated as:
[tex]\[ \text{Average Daily Balance} = \frac{(3 \text{ days} \times \$6390) + (27 \text{ days} \times \$0)}{30 \text{ days}} \][/tex]
Simplifying further:
[tex]\[ \text{Average Daily Balance} = \frac{(3 \times 6390) + (27 \times 0)}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{19170 + 0}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = \frac{19170}{30} \][/tex]
[tex]\[ \text{Average Daily Balance} = 639 \][/tex]
2. Convert APR to Daily Percentage Rate:
- The Annual Percentage Rate (APR) is 17%, which is equivalent to 0.17 as a decimal.
- The daily percentage rate is calculated by dividing the APR by the number of days in a year (365 days):
[tex]\[ \text{Daily Interest Rate} = \frac{0.17}{365} \][/tex]
This simplifies to:
[tex]\[ \text{Daily Interest Rate} \approx 0.0004657534 \][/tex]
3. Calculate the Interest Charged:
- Using the previous balance method, the interest charged can be calculated using the formula:
[tex]\[ \text{Interest} = \text{Daily Interest Rate} \times \text{Number of Days in Billing Cycle} \times \text{Average Daily Balance} \][/tex]
Plugging in the values from our calculations:
[tex]\[ \text{Interest} = 0.0004657534 \times 30 \times 639 \][/tex]
Simplifying further:
[tex]\[ \text{Interest} = 0.0004657534 \times 19170 \][/tex]
[tex]\[ \text{Interest} \approx 8.928493 \][/tex]
4. Choose the Correct Expression:
We look for the expression that matches the calculation steps we have taken. The correct expression is:
A. [tex]\(\left(\frac{0.17}{365} \cdot 30\right)\left(\frac{3 \cdot \$ 6390+27 \cdot \$ 0}{30}\right)\)[/tex]
This matches perfectly with our step-by-step solution. Therefore, the correct expression to calculate the amount Joan was charged in interest for the billing cycle is:
Option A: [tex]\(\left(\frac{0.17}{365} \cdot 30\right)\left(\frac{3 \cdot \$ 6390+27 \cdot \$ 0}{30}\right)\)[/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
