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?]单项选择题
A
32.77
B
32.86
C
32.94
D
32.56

Question

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?]单项选择题

A

32.77

B

32.86

C

32.94

D

32.56

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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类似问题

A customer of a bank has $275,000 in surplus funds that need to be invested for a short period of time. The bank offers to sell a 90-day negotiable certificate of deposit (CD) to the customer at a yield of 6.45 per cent per annum. Advise the customer of the dollar return on the CD.

A bank, in a 365-day year country, accepts a $2m deposit to mature in 270 days and will pay 2.33% p.a. on the deposit. How much interest will it pay?

Interest on a savings account is calculated at 0.3% per month based on the minimum monthly balance. The following statement lists all the transactions on an account for January–March one year. The interest, in dollars, for the month of February is:

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更多留学生实用工具

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