Harvey has a credit card that uses the previous balance method. The opening balance of one of his 30-day billing cycles was $2790, but that was his balance for only the first 6 days of the billing cycle, because he then paid off his entire balance and didn't make any new purchases. If his credit card's APR is [tex]$21 \%$[/tex], which of these expressions could be used to calculate the amount Harvey was charged in interest for the billing cycle?
A. [tex]\left(\frac{0.21}{365} \cdot 30\right)\left(\frac{6 \cdot \$ 2790+24 \cdot \$ 0}{30}\right)[/tex]
B. [tex]\left(\frac{0.21}{365} \cdot 30\right)(\$ 0)[/tex]
C. [tex]\left(\frac{0.21}{365} \cdot 30\right)(\$ 2790)[/tex]
D. [tex]\left(\frac{0.21}{365} \cdot 30\right)\left(\frac{6 \cdot \$ 0+24 \cdot \$ 2790}{30}\right)[/tex]
Answer (2)
The expression to calculate Harvey's interest is ( 365 0.21 ⋅ 30 ) ( 30 6 ⋅ 2790 + 24 ⋅ 0 ) , which represents the calculation based on his average daily balance. This matches option A. Calculating interest in this way helps understand how long balances affect costs over time.
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Calculate the average daily balance: 30 6 × $2790 + 24 × $0 .
Determine the daily interest rate: 365 0.21 .
Calculate the interest charged: 365 0.21 × 30 × 30 6 × $2790 + 24 × $0 .
The expression that matches the calculation is: ( 365 0.21 ⋅ 30 ) ( 30 6 ⋅ $2790 + 24 ⋅ $0 ) .
Explanation
Understanding the Problem Harvey's credit card uses the previous balance method, and we need to determine the correct expression to calculate the interest charged for the billing cycle. The opening balance was $2790 for the first 6 days, and then it was $0 for the remaining 24 days of the 30-day billing cycle. The APR is 21%.
Calculating the Average Daily Balance First, we need to calculate the average daily balance. Since the balance was $2790 for 6 days and $0 for 24 days, the average daily balance is calculated as follows: 30 6 × $2790 + 24 × $0 = 30 $16740 = $558 So, the average daily balance is $558.
Calculating the Daily Interest Rate Next, we need to find the daily interest rate. The APR is 21%, so the daily interest rate is: 365 0.21
Calculating the Interest Charged Now, we can calculate the interest charged for the billing cycle by multiplying the average daily balance by the daily interest rate and the number of days in the billing cycle (30 days): Interest = 365 0.21 × 30 × $558 = 365 0.21 × 30 × 30 6 × $2790 + 24 × $0
Identifying the Correct Expression Comparing this expression with the given options, we see that option A matches our calculated expression: A. ( 365 0.21 ⋅ 30 ) ( 30 6 ⋅ $2790 + 24 ⋅ $0 )
Final Answer Therefore, the correct expression to calculate the amount Harvey was charged in interest for the billing cycle is: ( 365 0.21 ⋅ 30 ) ( 30 6 ⋅ $2790 + 24 ⋅ $0 )
Examples
Understanding credit card interest calculations is crucial for managing personal finances. For instance, if you carry a balance on your credit card, the interest charged is calculated based on your average daily balance. Knowing how this interest is calculated helps you make informed decisions about paying off your balance and avoiding unnecessary charges. This is particularly useful when planning your budget and making financial forecasts, ensuring you can effectively manage your debt and save money.
