In a company's first year in operation, it made an annual profit of $112, 000. The profit of the
company increased at a constant 18% per year each year. How much total profit would the compan
make over the course of its first 26 years of operation, to the nearest whole number?
To find the total profit the company would make over the course of its first 26 years of operation, we first need to find the profit for each individual year.
The profit for the first year is $112,000.
For each subsequent year, the profit increases by 18% compared to the previous year.
To calculate the profit for each year, we can use the formula:
Profit for current year = Profit for previous year + (Profit for previous year * 18%)
So, for the second year:
Profit for second year = $112,000 + ($112,000 * 0.18) = $132,160
For the third year:
Profit for third year = $132,160 + ($132,160 * 0.18) = $155,654.40
We can continue this calculation for each subsequent year, increasing the profit by 18% each time.
Now, we need to find the total profit over 26 years. We can do this by adding up the profit for each year.
Total profit = Profit for year 1 + Profit for year 2 + Profit for year 3 + ... + Profit for year 26
Total profit = $112,000 + $132,160 + $155,654.40 + ...
To make this calculation easier, we can use the formula for the sum of a geometric series:
Sum = a * (1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = $112,000, r = 1 + 0.18 = 1.18, and n = 26.
Using these values in the formula, we can calculate the total profit:
Total profit = $112,000 * (1 - 1.18^26) / (1 - 1.18)
Total profit ≈ $8,006,948
Therefore, the company would make a total profit of approximately $8,006,948 over the course of its first 26 years of operation.