A hardware store makes a profit of $41,000 during its first year. The store owner sets a goal of increasing profits by $9000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.
looks like an arithmetic series with
a = 41000 , d = 9000, n = 5
find Sum(5) using the formula.
Confirm by just adding up the first 5 terms.
To find the total profit during the first 5 years of business, we need to calculate the profits for each of the 5 years and then sum them up.
Given that the store makes a profit of $41,000 during its first year, we can directly add this to the total profit.
Profit in the first year = $41,000
Now, the store owner sets a goal of increasing profits by $9000 each year for the next 4 years. We can calculate the profit for each of these 4 years based on this goal.
Profit in the second year = profit in the first year + increase for the second year
Profit in the second year = $41,000 + $9,000 = $50,000
Profit in the third year = profit in the second year + increase for the third year
Profit in the third year = $50,000 + $9,000 = $59,000
Profit in the fourth year = profit in the third year + increase for the fourth year
Profit in the fourth year = $59,000 + $9,000 = $68,000
Profit in the fifth year = profit in the fourth year + increase for the fifth year
Profit in the fifth year = $68,000 + $9,000 = $77,000
Now, to find the total profit during the first 5 years, we add up the profits for each of the 5 years:
Total profit = profit in the first year + profit in the second year + profit in the third year + profit in the fourth year + profit in the fifth year
Total profit = $41,000 + $50,000 + $59,000 + $68,000 + $77,000
Total profit = $295,000
Therefore, the total profit during the first 5 years of business is $295,000.