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Shirley has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was [tex]$\$[/tex]2830[tex]$, but that was her balance for only the first 2 days of the billing cycle because she then paid off her entire balance and didn't make any new purchases. If her credit card's APR is $[/tex]19\%[tex]$, which of these expressions could be used to calculate the amount Shirley was charged in interest for the billing cycle?

A. $[/tex]\left(\frac{0.19}{365} \cdot 30\right)\left(\frac{2 \cdot 2830 + 28 \cdot 0}{30}\right)[tex]$
B. $[/tex]\left(\frac{0.19}{365} \cdot 30\right)\left(\frac{2 \cdot 2890 + 28 \cdot 0}{30}\right)[tex]$
C. $[/tex]\left(\frac{0.19}{350} \cdot 30\right)(30)[tex]$
D. $[/tex]\left(\frac{0.19}{355} \cdot 30\right)(\[tex]$2830)$[/tex]

Sagot :

GinnyAnswer
To determine the amount Shirley was charged in interest for the billing cycle, we need to use the Previous Balance Method given her situation:

1. Identify the Important Variables:
- Opening balance: \[tex]$2830 - Annual Percentage Rate (APR): 19% or 0.19 - Days in the billing cycle: 30 - Days with the balance: 2 2. Calculate the Daily Interest Rate: Since the APR is given annually, we need to convert this to a daily rate. \( \text{Daily Interest Rate} = \frac{\text{APR}}{365} \) 3. Calculate the Interest Charged: Using the previous balance method, we multiply the opening balance by the daily interest rate, and then multiply by the number of days the balance was held. \( \text{Interest} = \text{Opening Balance} \times \text{Daily Interest Rate} \times \text{Days With Balance} \) 4. Input the Variables: - Opening Balance = \$[/tex]2830
- APR = 0.19
- Daily Interest Rate = [tex]\(\frac{0.19}{365}\)[/tex]
- Days With Balance = 2

5. Calculate the Daily Interest Rate:
[tex]\( \text{Daily Interest Rate} = \frac{0.19}{365} \approx 0.00052055 \)[/tex]

6. Calculate the Interest Charged:
[tex]\( \text{Interest} = 2830 \times 0.00052055 \times 2 \approx 2.9463 \)[/tex]

Let's compare these steps to the given expressions:

A. [tex]\(\left(\frac{0.19}{3 \infty 6} \cdot 30\right)\left(\frac{2 \cdot 30+28 \cdot 32800}{30}\right)\)[/tex]

B. [tex]\(\left(\frac{0.19}{365} \cdot 30\right)\left(\frac{2 \cdot\{2890+28 \cdot \$ 0}{30}\right)\)[/tex]

C. [tex]\(\left(\frac{0.19}{350} \cdot 30\right)(30)\)[/tex]

D. [tex]\(\left(\frac{0.19}{355} \cdot 30\right)(\$ 2 B 50)\)[/tex]

Clearly, Option B fits our calculations:

- The term [tex]\(\frac{0.19}{365} \cdot 30\)[/tex] simplifies to the effective APR part over 30 days (though we actually do not multiply by 30 directly but leaving it takes part as bias).
- The term [tex]\(\frac{2 \cdot 2830 + 28 \cdot 0}{30}\)[/tex] simplifies to the average daily balance over the cycle, which accurately represents the situation specified (though strictly not necessary since [tex]\(\cdot 0\)[/tex] part denoting zero purchases).

So given all our calculations, it's apparent that the expression capable of calculating the interest Shirley must pay is:

Answer: B. \(\left(\frac{0.19}{365} \cdot 30\right)\left(\frac{2 \cdot 2830 + 28 \cdot 0}{30}\right)
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