Question

A company has revenues of $100 during Year 1. Each year their profit is 20% of revenue. Revenue is growing 15% per year. How much total profit (rounded to the nearest penny) will the company earn during Years 1-10

Answer 1

To calculate the total profit a company will earn over 10 years, we calculate the yearly revenue growth due to a 15% increase, take 20% of that as profit, and sum the profits over the years. We use the formula for compound growth for the revenue and then apply the profit margin to determine yearly profits. The sum of these profits yields the total profit.

Step-by-step explanation:

The question involves calculating the total profit a company will earn over a period of 10 years, given that the company has a revenue growth rate of 15% per year and a profit margin of 20% of revenue. To answer this, we use the formula for compound interest to determine the revenue for each year, and then calculate 20% of that revenue to find the profit for that year. We will sum up the profits for all 10 years to get the total profit.

1. Determine the revenue for Year 1, which is given as $100.
2. For each subsequent year, increase the previous year's revenue by 15%. Revenue for Year n (R_n) is calculated as R_n = R_(n-1) x (1 + 0.15).
3. Calculate 20% of each year's revenue to find the profit for that year.
4. Sum all the yearly profits to get the total profit for the 10 years.

Assuming P_n represents the profit in Year n, the calculation for the first three years would look like:

• P_1 = $100 x 0.20 = $20
• P_2 = $100 x (1 + 0.15) x 0.20
• P_3 = $100 x (1 + 0.15)^2 x 0.20

Repeat this process for each year up to Year 10, and then add them together for the total profit over the 10 years. Remember to round to the nearest penny when providing the final total profit number.