Answer:
To find the principal in each account, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Let's start with Account A:
Interest earned in Account A = $6.30
Rate for Account A = 3.6% = 0.036 (as a decimal)
Time for Account A = 21 months
Using the formula, we can rearrange it to solve for the principal:
Principal for Account A = Interest / (Rate * Time)
Principal for Account A = $6.30 / (0.036 * 21)
Principal for Account A ≈ $50
So, the principal in Account A is approximately $50.
Now let's move on to Account B:
Interest earned in Account B = $34.65
Rate for Account B = 2.2% = 0.022 (as a decimal)
Time for Account B = 27 months
Using the same formula:
Principal for Account B = Interest / (Rate * Time)
Principal for Account B = $34.65 / (0.022 * 27)
Principal for Account B ≈ $300
So, the principal in Account B is approximately $300.
Now, let's compare the interest earned in the first month for each account. To do this, we need to calculate the interest earned for the first month separately for each account.
For Account A:
Principal = $50
Rate = 3.6% = 0.036 (as a decimal)
Time = 1 month
Interest earned in the first month for Account A = Principal * Rate * Time
Interest earned in the first month for Account A = $50 * 0.036 * 1 = $1.80
For Account B:
Principal = $300
Rate = 2.2% = 0.022 (as a decimal)
Time = 1 month
Interest earned in the first month for Account B = Principal * Rate * Time
Interest earned in the first month for Account B = $300 * 0.022 * 1 = $6.60
From the calculations, we can see that Account B earned more interest in the first month with $6.60 compared to Account A's $1.80.
Therefore, the principal in Account A is approximately $50, and the principal in Account B is approximately $300. Account B earned the most interest in the first month with $6.60.