Final answer:
Using the formula for simple interest, the principal for Account A was found to be $250.00, while the principal for Account B was $625.00. Contrary to initial assumption based on rates, Account B earned more interest in the first month because it had a larger principal.
Step-by-step explanation:
To calculate the principal for each account, we can use the formula for simple interest: Interest = Principal × Rate × Time. Since we're given the interest earned for each account, the annual interest rate, and the time period in months, we can rearrange this formula to solve for the principal.
For Account A, the simple interest is $11.25, the rate is 3.6%, and the time is 15 months (or 15/12 years). We can calculate the principal as follows:
11.25 = Principal × (3.6/100) × (15/12)
Principal = 11.25 / ((3.6/100) × (15/12))
Principal = $250.00
For Account B, the simple interest is $13.75, the rate is 2.2%, and the time is the same 15 months. The principal for Account B would be:
13.75 = Principal × (2.2/100) × (15/12)
Principal = 13.75 / ((2.2/100) × (15/12))
Principal = $625.00
To determine which account earned more interest in the first month, we can compare the monthly interest for each account. Account A would earn more in the first month because it has a higher interest rate (3.6% vs 2.2%), hence the simple interest for the first month would be:
For Account A: $250 × (3.6/100) × (1/12) = $0.75
For Account B: $625 × (2.2/100) × (1/12) = $1.15
Contrary to the initial assumption, Account B actually earns more interest in the first month due to its larger principal despite a lower interest rate.