9
QuizMultiple Choice

The Business Plan

Question 9 • FowU - Financial Math - B

Sam is planning to start a pool cleaning business. He expect to make a profit of $45,000 in his first year of business, after which he expects profits to increase by 5.5% annually for the next 5 years.Sam's business will cost $49,500 to set up and run for the first year. Sam then expects an annual operational expense total of $30,500. According to Sam's model, how long will it take Sam to see an overall profit in his business (where total profits exceed total expenses)?

Answer
A
Sam will see an overall profit in his first year of business.
B
Sam will see an overall profit in his second year of business.
C
Sam will see an overall profit in his third year of business.
D
Sam will see an overall profit in his fourth year of business.

Explanation

In the first year, Sam’s $45,000 profit is $4,500 less than the $49,500 setup and first-year cost. In year two, his profit rises to $45,000 × 1.055 = $47,475, and expenses are $30,500, so he gains $16,975 that year. That more than makes up the first-year shortfall, so his cumulative profits exceed his cumulative expenses in the second year: choice b, “Sam will see an overall profit in his second year of business.”

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