Let \(x\) be the amount invested in Account A, and \(33,000 - x\) be the amount invested in Account B.
Interest earned by Account A (at 5%): \(0.05x\)
Interest earned by Account B (at 3%): \(0.03( 33,000 - x) \)
According to the problem, the interest earned by Account A is twice the interest earned by Account B:
\[0.05x = 2 \times 0.03( 33,000 - x) \]
Solving for \(x\):
\[0.05x = 0.06( 33,000 - x) \]
\[0.05x = 1,980 - 0.06x\]
\[0.05x + 0.06x = 1,980\]
\[0.11x = 1,980\]
\[x = \frac { 1,980} { 0.11} \]
\[x = 18,000\]
So, \(33,000 - x = 33,000 - 18,000 = 15,000\).
Now, calculate the total interest:
Interest from Account A: \(0.05 \times 18,000 = 900\)
Interest from Account B: \(0.03 \times 15,000 = 450\)
Total interest: \(900 + 450 = 1,350\)
Thus, the total interest earned by the 2 accounts for the first year is $1,320.

Supplemental Knowledge

When dealing with investments and interest rates, it's essential to understand the basic formula for calculating simple interest:
\[\text { Interest} = \text { Principal} \times \text { Rate} \times \text { Time} \]
Where:

Principal is the initial amount of money invested.

Rate is the annual interest rate (expressed as a decimal).

Time is the period of time the money is invested for (in years).
In this problem, Alfredo has invested in two accounts with different interest rates. The relationship between the interests earned by these accounts provides a system of equations that can be solved to find out how much was invested in each account.

Theory in Practice

Imagine having two savings accounts that offer differing interest rates; by strategically allocating savings between them, you could maximize the total interest earned and inform future financial decisions more accurately. Acknowledging and understanding interest calculations helps make smart financial choices.

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