The APR on a credit card is 19.99%. Assume that, on 1 April 2024, there was a carry over balance of $2,000, and that the card was not used at all in April 2024 (thus, the balance on every day in April 2024 is $2,000). Compute the interest charged on this card for the entire month of April 2024. Assume that the interest is computed based on the daily interest rate. [Be careful - is 2024 a leap year?]

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BlackTom AI · Accepted Answer

We start by identifying the key values: APR = 19.99%, balance = $2,000 maintained for the entire April 2024, and April has 30 days. Since 2024 is a leap year, we use 366 days for the daily interest calculation.

Step 1: Compute the daily interest rate. The daily rate is the annual rate divided by the number of days in the year: 0.1999 / 366 ≈ 0.0005459 (in decimal form). As a percentage, this is about 0.05459% per day.

Step 2: Compute daily interest on the balance. Daily interest = balance × daily rate = $2,000 × 0.0005459 ≈ $1.0918.

Step 3: Compute total interest for April. Interest for 30 days ≈ $1.0918 × 30 ≈ $32.754 (approximately $32.75 to $32.76 range depending on rounding).

Now evaluate the answer choices:
- Option 32.77: This is a close match to the computed value after rounding. If we round daily interest to $1.092 and multiply by 30 days, we get $32.76; using a slightly more precise daily rate or rounding method can yield $32.77, which aligns with standard rounding rules.
- Option 32.86: This would require a higher daily rate or more days than 30, which contradicts the given data (30 days in April) and the calculated daily rate slightly below 0.000546. It overestimates the total.
- Option 32.94: Similar to 32.86, this is too high given the computed daily interest and the 30-day period.
- Option 32.56: This is slightly lower than the calculation using the precise daily rate and typical rounding; it would occur if one used a marginally smaller daily rate or truncated at an earlier step, but it diverges from the standard calculation with 366-day year.

In summary, because April has 30 days and 2024 is a leap year (366 days) for daily interest calculation, the total interest comes out to about $32.75–$32.77, with 32.77 being the option that best matches the precise calculation and rounding conventions.

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