Pearl has a credit card that uses the adjusted balance method. For the first 10 days of one of her 30-day billing cycles, her balance was $1120. She then made a purchase for $340, so her balance jumped to $1460, and it remained that amount for the next 10 days. Pearl then made a payment of $580, so her balance for the last 10 days of the billing cycle was $880. If her credit card's APR is 27%, which of these expressions could be used to calculate the amount Pearl was charged in interest for the billing cycle?
A. [tex]\left(\frac{0.27}{365} \cdot 30\right)\left(\frac{10 \cdot \$ 1120+10 \cdot \$ 1460+10 \cdot \$ 580}{30}\right)[/tex]
B. [tex]\left(\frac{0.27}{365} \cdot 30\right)\left(\frac{10 \cdot \$ 1120+10 \cdot \$ 1460+10 \cdot \$ 880}{30}\right)[/tex]
C. [tex]\left(\frac{0.27}{365} \cdot 30\right)(\$ 1120)[/tex]
D. [tex]\left(\frac{0.27}{365} \cdot 30\right)(\$ 540)[/tex]
Answer (2)
To calculate the interest charged to Pearl's credit card, we find her average daily balance and apply the daily interest rate based on her APR. The correct expression for calculating the interest is option A: ( 365 0.27 ⋅ 30 ) ( 30 10 ⋅ 1120 + 10 ⋅ 1460 + 10 ⋅ 880 ) . This method effectively accounts for the varying balance throughout the billing cycle.
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Calculate the average daily balance: 30 10 × $1120 + 10 × $1460 + 10 × $880 .
Determine the daily interest rate: 365 0.27 .
Calculate the interest for the billing cycle: 365 0.27 × 30 × 30 10 × $1120 + 10 × $1460 + 10 × $880 .
The correct expression is: ( 365 0.27 ⋅ 30 ) ( 30 10 ⋅ $1120 + 10 ⋅ $1460 + 10 ⋅ $880 ) .
Explanation
Understanding the Problem Let's break down this problem. We need to find the expression that calculates the interest Pearl was charged using the adjusted balance method. This method calculates interest based on the average daily balance.
Calculating the Average Daily Balance First, we need to calculate the average daily balance. Pearl's balance was $1120 for 10 days, $1460 for the next 10 days, and 880 f or t h e l a s t 10 d a ys . S o , t h e a v er a g e d ai l y ba l an ce i sc a l c u l a t e d a s : 30 10 × 1120 + 10 × 1460 + 10 × 880 T hi ss im pl i f i es t o : 30 11200 + 14600 + 8800 = 30 34600 = 1153.33 $
So, the average daily balance is approximately $1153.33.
Calculating the Daily Interest Rate Next, we need to calculate the daily interest rate. The APR is 27%, so the daily interest rate is: 365 0.27
Calculating the Interest for the Billing Cycle Now, we calculate the interest for the entire billing cycle by multiplying the average daily balance by the daily interest rate and the number of days in the billing cycle (30): Interest = 365 0.27 × 30 × 30 10 × 1120 + 10 × 1460 + 10 × 880 This matches option B.
Final Answer Therefore, the expression that could be used to calculate the amount Pearl was charged in interest for the billing cycle is: ( 365 0.27 ⋅ 30 ) ( 30 10 ⋅ $1120 + 10 ⋅ $1460 + 10 ⋅ $880 )
Examples
Understanding credit card interest calculations is crucial for managing personal finances. For instance, if you carry a balance on your credit card, knowing how the interest is calculated helps you estimate the cost of borrowing. This knowledge enables you to make informed decisions about paying off your balance faster, potentially saving you money on interest charges. Additionally, understanding these calculations can help you compare different credit card offers and choose the one that best suits your financial needs. For example, if Pearl knows that her average daily balance is $1153.33, she can calculate her monthly interest charges and plan her payments accordingly.
