Final answer:
The person has put $594 into the bank account by December 30.
Step-by-step explanation:
To find the total amount of money that the person has put into the bank account by December 30, we need to find the sum of all the deposits made from January 1 to December 30.
Since the person is depositing the money on a monthly basis, we can find the total amount by finding the sum of an arithmetic sequence.
First, let's find the common difference, which is the amount of money added each month. In this case, the common difference is $5 because the person is adding $5 more each month.
Next, we need to find the number of terms in the sequence. Since the person is depositing money for 12 months, there are 12 terms in the sequence.
Now, we can find the sum of the arithmetic sequence using the formula: S = n/2 * (2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
Plugging in the values, we have: S = 12/2 * (2 * 22 + (12-1) * 5)
Simplifying the equation, we get: S = 6 * (44 + 11 * 5) = 6 * (44 + 55) = 6 * 99 = 594
Therefore, the person has put $594 into the bank account by December 30.