Question

Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with a $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? A = P (1 + r) superscript t
a.
Korey will see an overall profit in his first year of business.
b.
Korey will see an overall profit in his second year of business.
c.
Korey will see an overall profit in his third year of business.
d.
Korey will see an overall profit in his fourth year of business.

Answer 1

Answer: b.

Reason: The given $12,000 is profit (net of the $8,000 annual operating cost), so only the $12,500 opening cost remains to be recouped. Profits form a geometric sequence: year 1 = 12,000, year 2 = 12,000(1.06) = 12,720. Cumulative after 2 years = 12,000 + 12,720 = 24,720, which exceeds the $12,500 opening cost. So he sees an overall profit in the second year.