Final answer:
To find the principal of each account, the formula Principal = Interest / (Rate × Time) can be used. Account A has a principal of $53.24 and Account B has a principal of $132.77. Account B earned the most interest in the first month, with $0.24.
Step-by-step explanation:
To find the principal in each account, we can use the formula for simple interest: Principal = Interest / (Rate × Time).
For Account A, the interest earned after 9 months is $6.94 and the interest rate is 3.7%. Using the formula, we have: Principal A = $6.94 / (0.037 × 9) = $53.24.
For Account B, the interest earned after 18 months is $13.80 and the interest rate is 2.3%. Using the formula, we have: Principal B = $13.80 / (0.023 × 18) = $132.77.
To determine which account earned the most interest in the first month, we can calculate the interest for the first month using the formula: Interest = Principal × Rate × (Time / 12).
Comparing Account A and Account B, we have:
Interest A = $53.24 × 0.037 × (1 / 12) = $0.13 (rounded to two decimal places)
Interest B = $132.77 × 0.023 × (1 / 12) = $0.24 (rounded to two decimal places)
Therefore, Account B earned the most interest in the first month with $0.24.