Question

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)?
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.


Please select the best answer from the choices provided

A
B
C
D

Answer 1

B

Year 1: profit = 45,000; expense = 49,500 → cumulative net = -4,500 (loss).
Year 2: profit = 45,000·1.055 = 47,475.
Cumulative profit = 45,000 + 47,475 = 92,475.
Cumulative expense = 49,500 + 30,500 = 80,000.
Cumulative net = 92,475 − 80,000 = 12,475 (positive), so overall profit occurs in year 2.