Question
marlene 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 $570. she then made a purchase for $120, so her balance jumped to $690, and it remained that amount for the next 10 days. marlene then made a payment of $250, so her balance for the last 10 days of the billing cycle was $440. if her credit card's APR is 15%, which of these expressions could be used to calculate the amount marlene was charged in interest for the billing cycle?
A. (0.15/365 * 30)($570)
B. (0.15/365 *30)($320)
C. (0.15/365 * 30)(10 * $570 + 10 * $690 + 10 * $440/30)
D. (0.15/365 * 30)(10 * $570 + 10 * $690 + 10 * $250/30)
A. (0.15/365 * 30)($570)
B. (0.15/365 *30)($320)
C. (0.15/365 * 30)(10 * $570 + 10 * $690 + 10 * $440/30)
D. (0.15/365 * 30)(10 * $570 + 10 * $690 + 10 * $250/30)
Answers
GPT-4o mini
To calculate the interest charged on Marlene's credit card balance using the adjusted balance method, we need to consider how long each balance was held during the billing cycle.
1. **First 10 days**: Marlene's balance was $570.
2. **Next 10 days**: After a purchase, her balance was $690.
3. **Last 10 days**: After a payment, her balance was $440.
We need to calculate the weighted average of the balances held over the billing cycle:
- For the first 10 days, she had a balance of $570.
- For the next 10 days, she had a balance of $690.
- For the last 10 days, she had a balance of $440.
The total interest charged for the billing cycle can be calculated using the formula:
\[
\text{Interest} = \text{APR} \times \text{(Average Balance)} \times \text{(Days in Billing Cycle) / 365}
\]
Where the average balance is found by accounting for the time each balance was at play:
- The contribution of the first balance is \(10 \times 570\)
- The contribution of the second balance is \(10 \times 690\)
- The contribution of the third balance is \(10 \times 440\)
Thus, the total average balance over 30 days is:
\[
\text{Average Balance} = \frac{(10 \times 570) + (10 \times 690) + (10 \times 440)}{30}
\]
This calculation correctly accounts for how long each balance was outstanding, essentially giving weight to the balance by the number of days it was held.
Now, we can evaluate the options provided:
- **Option A**: This only considers the first balance, which is incorrect.
- **Option B**: This uses $320, which is the difference, but it doesn't consider the correct average balance calculation.
- **Option C**: This is correct. It incorporates all balances weighted by the number of days they were maintained and divides appropriately.
- **Option D**: This incorrectly uses $250, which does not represent the correct balance for the last 10 days in context.
Thus, **option C** is the correct expression to calculate the amount Marlene was charged in interest for the billing cycle:
**C. \((0.15/365 \times 30)(10 \times 570 + 10 \times 690 + 10 \times 440/30)\)**
1. **First 10 days**: Marlene's balance was $570.
2. **Next 10 days**: After a purchase, her balance was $690.
3. **Last 10 days**: After a payment, her balance was $440.
We need to calculate the weighted average of the balances held over the billing cycle:
- For the first 10 days, she had a balance of $570.
- For the next 10 days, she had a balance of $690.
- For the last 10 days, she had a balance of $440.
The total interest charged for the billing cycle can be calculated using the formula:
\[
\text{Interest} = \text{APR} \times \text{(Average Balance)} \times \text{(Days in Billing Cycle) / 365}
\]
Where the average balance is found by accounting for the time each balance was at play:
- The contribution of the first balance is \(10 \times 570\)
- The contribution of the second balance is \(10 \times 690\)
- The contribution of the third balance is \(10 \times 440\)
Thus, the total average balance over 30 days is:
\[
\text{Average Balance} = \frac{(10 \times 570) + (10 \times 690) + (10 \times 440)}{30}
\]
This calculation correctly accounts for how long each balance was outstanding, essentially giving weight to the balance by the number of days it was held.
Now, we can evaluate the options provided:
- **Option A**: This only considers the first balance, which is incorrect.
- **Option B**: This uses $320, which is the difference, but it doesn't consider the correct average balance calculation.
- **Option C**: This is correct. It incorporates all balances weighted by the number of days they were maintained and divides appropriately.
- **Option D**: This incorrectly uses $250, which does not represent the correct balance for the last 10 days in context.
Thus, **option C** is the correct expression to calculate the amount Marlene was charged in interest for the billing cycle:
**C. \((0.15/365 \times 30)(10 \times 570 + 10 \times 690 + 10 \times 440/30)\)**