Mr. Lutta's salary starts at sh. 42,000 and increases by 13% annually. Calculate his total earnings over 15 years, rounded to the nearest thousand.

Here are the solutions to the problems.

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The initial salary of Mr. Lutta is sh. 42,000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands.

Step 1: Identify the given values and the type of progression.
This is a geometric progression.
The first term (initial salary) is $A = 42000$ sh.
The common ratio (1 + increase rate) is $r = 1 + 0.13 = 1.13$.
The number of years is $n = 15$.
We need to find the sum of the first 15 terms