Question

A company has revenue of $1000 in 2009. Our current estimate is that revenues will grow 25% per year. Our profit each year will equal 20% of revenue. What annual growth rate (rounded to the nearest 1%) in revenue would yield a total profit of $15,000 for years 2009-2015 for this situation. Enter just the number; e.g., 65%.

Answer 1

85.3%

Step-by-step explanation:

since profits = 20% of total revenue, so total revenue = $15,000 / 20% = $75,000

That means that total revenue must grow from $1,000 to $75,000 in just 7 years. We can use the future value formula to determine the growth rate:

future value = present value x (1 + r)ⁿ

$75,000 = $1,000 x (1 + r)⁷

(1 + r)⁷ = $75,000 / $1,000 = 75

⁷√(1 + r)⁷ = ⁷√75

1 + r = 1.853

r = 1.853 - 1 = 0.853 = 85.3%