To find out how much will be withdrawn from the messenger's salary in the last month, we need to calculate the increasing amount each month.
In this scenario, the amount to be withdrawn each month follows an arithmetic progression, with a common difference of #5,000.
To find the amount to be withdrawn in the last month, we need to find the 12th term of the arithmetic progression.
The formula to find the nth term of an arithmetic progression is given by:
a_n = a + (n - 1)d
Where:
- a is the first term of the progression
- n is the term number we are looking for
- d is the common difference
In this case:
- a = 5000 (first term, amount withdrawn from the 1st month)
- n = 12 (we are looking for the 12th month)
- d = 5000 (common difference, each month's amount increases by #5,000)
Substituting the values into the formula, we get:
a_{12} = 5000 + (12 - 1) \cdot 5000
Simplifying further:
a_{12} = 5000 + 11 \cdot 5000
a_{12} = 5000 + 55000
a_{12} = 60000
Therefore, #60,000 will be withdrawn from the messenger's salary in the last month.
Answer: \boxed{60000}.