Discover new information and insights with the help of IDNLearn.com. Our platform offers comprehensive and accurate responses to help you make informed decisions on any topic.
Sagot :
Let's solve the problem step-by-step to determine the correct expression for calculating the interest charged to Norma's credit card for the given billing cycle.
1. Understand the balances over the billing cycle:
- For the first 10 days: Balance = [tex]$1850 - For the next 10 days after making a purchase: Balance = $[/tex]2010 (after a [tex]$160 purchase) - For the last 10 days after making a payment: Balance = $[/tex]1080 (after a [tex]$930 payment) 2. Calculate the average daily balance for the 30-day billing cycle: The formula to find the average daily balance over the entire billing cycle is: \[ \text{Average Daily Balance} = \frac{(\text{Balance}_1 \times \text{Days}_1) + (\text{Balance}_2 \times \text{Days}_2) + (\text{Balance}_3 \times \text{Days}_3)}{\text{Total Days}} \] Substituting the values given: \[ \text{Average Daily Balance} = \frac{(1850 \times 10) + (2010 \times 10) + (1080 \times 10)}{30} \] Simplifying step-by-step: \[ (1850 \times 10) = 18500 \] \[ (2010 \times 10) = 20100 \] \[ (1080 \times 10) = 10800 \] Adding them together: \[ 18500 + 20100 + 10800 = 49400 \] Now, divide by the total number of days: \[ \text{Average Daily Balance} = \frac{49400}{30} = 1646.6667 \] 3. Convert annual percentage rate (APR) to daily interest rate: The APR given is 29%, so the daily interest rate is: \[ \text{Daily Interest Rate} = \frac{APR}{365} = \frac{0.29}{365} = 0.0007945205 \] 4. Calculate the total interest charged over the 30-day cycle: Multiply the daily interest rate by the number of days in the cycle and the average daily balance calculated above: \[ \text{Interest Charged} = \text{Daily Interest Rate} \times \text{Days in Cycle} \times \text{Average Daily Balance} \] Substituting the values we have: \[ \text{Interest Charged} = 0.0007945205 \times 30 \times 1646.6667 = 39.2493 \] 5. Identify the correct expression: From the given options, the expression closest to our derived expression is: \[ \left(\frac{0.29}{365} \cdot 30\right)\left(\frac{10 \cdot \$[/tex] 1850 + 10 \cdot \[tex]$ 2010 + 10 \cdot \$[/tex] 1080}{30}\right)
\]
This matches with Option A. Thus, the correct expression to calculate the interest Norma was charged is:
A.
[tex]\[ \left(\frac{0.29}{365} \cdot 30\right)\left(\frac{10 \cdot \$ 1850 + 10 \cdot \$ 2010 + 10 \cdot \$ 1080}{30}\right) \][/tex]
1. Understand the balances over the billing cycle:
- For the first 10 days: Balance = [tex]$1850 - For the next 10 days after making a purchase: Balance = $[/tex]2010 (after a [tex]$160 purchase) - For the last 10 days after making a payment: Balance = $[/tex]1080 (after a [tex]$930 payment) 2. Calculate the average daily balance for the 30-day billing cycle: The formula to find the average daily balance over the entire billing cycle is: \[ \text{Average Daily Balance} = \frac{(\text{Balance}_1 \times \text{Days}_1) + (\text{Balance}_2 \times \text{Days}_2) + (\text{Balance}_3 \times \text{Days}_3)}{\text{Total Days}} \] Substituting the values given: \[ \text{Average Daily Balance} = \frac{(1850 \times 10) + (2010 \times 10) + (1080 \times 10)}{30} \] Simplifying step-by-step: \[ (1850 \times 10) = 18500 \] \[ (2010 \times 10) = 20100 \] \[ (1080 \times 10) = 10800 \] Adding them together: \[ 18500 + 20100 + 10800 = 49400 \] Now, divide by the total number of days: \[ \text{Average Daily Balance} = \frac{49400}{30} = 1646.6667 \] 3. Convert annual percentage rate (APR) to daily interest rate: The APR given is 29%, so the daily interest rate is: \[ \text{Daily Interest Rate} = \frac{APR}{365} = \frac{0.29}{365} = 0.0007945205 \] 4. Calculate the total interest charged over the 30-day cycle: Multiply the daily interest rate by the number of days in the cycle and the average daily balance calculated above: \[ \text{Interest Charged} = \text{Daily Interest Rate} \times \text{Days in Cycle} \times \text{Average Daily Balance} \] Substituting the values we have: \[ \text{Interest Charged} = 0.0007945205 \times 30 \times 1646.6667 = 39.2493 \] 5. Identify the correct expression: From the given options, the expression closest to our derived expression is: \[ \left(\frac{0.29}{365} \cdot 30\right)\left(\frac{10 \cdot \$[/tex] 1850 + 10 \cdot \[tex]$ 2010 + 10 \cdot \$[/tex] 1080}{30}\right)
\]
This matches with Option A. Thus, the correct expression to calculate the interest Norma was charged is:
A.
[tex]\[ \left(\frac{0.29}{365} \cdot 30\right)\left(\frac{10 \cdot \$ 1850 + 10 \cdot \$ 2010 + 10 \cdot \$ 1080}{30}\right) \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.
