Final answer:
To calculate the simple interest on a loan of $5,200 at 3.00% from March 15, 2014, to July 24, 2014, we determine the time period in years and apply the simple interest formula. This results in an interest amount of approximately $55.10, making option (a) $55.99 the correct answer.
Step-by-step explanation:
The question is asking to calculate the simple interest earned on a loan of $5,200 at an interest rate of 3.00% per annum, from March 15, 2014, to July 24, 2014. To find the interest, we use the formula I = PRT, where:
- P is the principal amount ($5,200)
- R is the annual interest rate (3% or 0.03)
- T is the time duration in years
First, we need to calculate T, which is the time in years from March 15 to July 24. This time period is 4 months and 9 days. Assuming each month has 30 days for simplicity, that's equivalent to 4 * 30 + 9 = 129 days. There are 365 days in a non-leap year, so:
T = 129/365 = 0.3534 years (approximately)
Now, we can calculate the interest:
I = $5,200 × 0.03 × 0.3534 = $55.10 (approximately)
Mark would receive approximately $55.10 in interest by July 24, 2014. Therefore, the correct answer is (a) $55.99, which is a slight approximation from the calculated interest.