Derrick's dad buys new tires for $900 using a credit card that charges simple interest at an annual rate of 19%. He has no other charges on the card and does not pay off the balance at the end of the month. Assuming simple interest, how much interest will he owe after one month?

Introduction / Context:
This question illustrates how an annual percentage rate on a credit card translates into a charge for a shorter period such as one month. Understanding this helps consumers see how expensive high credit card rates can be, even over short intervals. The calculation is based on simple interest, which is a reasonable approximation over a single month when there are no additional purchases or payments.

Given Data / Assumptions:

Purchase amount and outstanding balance P = $900
Annual simple interest rate R = 19 percent per annum
Time outstanding T = 1 month
Assume simple interest with no compounding during the month
Assume a standard year of 12 months

Concept / Approach:
First, convert the annual rate into a decimal. Then convert one month into a fraction of a year, which is 1 / 12. Apply the simple interest formula I = P * R * T. The result gives the interest owed for one month. This method assumes that the balance remains unchanged during the month and that interest is not compounded over such a short period, which is typical in introductory quantitative problems.

Step-by-Step Solution:
Step 1: Convert annual rate to decimal. R = 19 percent = 19 / 100 = 0.19. Step 2: Express one month as a fraction of a year. T = 1 month = 1 / 12 years. Step 3: Use the simple interest formula I = P * R * T. I = 900 * 0.19 * (1 / 12). Step 4: Compute product: 900 * 0.19 = 171 dollars per year. Step 5: Divide by 12 for one month: I = 171 / 12 = 14.25 dollars.

Verification / Alternative check:
To verify, approximate 20 percent of 900, which is 180 dollars per year. Nineteen percent is slightly less, at 171 dollars per year. Since one month is roughly one twelfth of a year, the interest should be about 171 / 12, which is just over 14 dollars. The exact calculation gives 14.25 dollars, confirming the accuracy and indicating that the answer is in a reasonable range for the given rate and principal.

Why Other Options Are Wrong:
Option $11.25 would correspond to a lower annual rate, closer to 15 percent, not 19 percent. Option $13.25 underestimates the fraction of 171 dollars for one month. Option $15.25 overestimates the interest and would correspond to a slightly higher effective annual rate than 19 percent. Only $14.25 exactly matches the simple interest computation for one month at 19 percent on a 900 dollar balance.

Common Pitfalls:
Some learners mistakenly use T = 1 instead of 1 / 12, effectively charging a full year of interest for a single month. Others incorrectly divide by 10 or by 100 instead of 12 when converting the annual figure into a monthly one. There can also be confusion between simple and compound interest, but for one month on a fixed balance, both will be very similar. Carefully converting time and rate units is essential for correct answers.

Final Answer:
The interest owed after one month on the credit card purchase is $14.25.