The chief financial officer of a company reports that profits for the past fiscal year were $17.5 million.The officer predicts that profits for the next 7 years will grow at a continuous annual rate somewhere between % and 9%.Estimate the cumulative difference in total profit over the 7 years based on the predicted range of growth rates.Round your answer to three decimal places.

Question

The chief financial officer of a company reports that profits for the past fiscal year were $17.5 million.The officer predicts that profits for the next 7 years will grow at a continuous annual rate somewhere between  % and 9%.Estimate the cumulative difference in total profit over the 7 years based on the predicted range of growth rates.Round your answer to three decimal places. ​

Quizplus · Accepted Answer

To estimate the cumulative difference in total profit, we can use the formula for continuous growth:

P(t) = P0 * e^(rt)

Where:
P0 = initial profit ($17.5 million)
r = annual growth rate
t = time (in years)

We want to find the difference in total profit over 7 years between the high and low end of the predicted growth rate range:

High end: P(7) = 17.5 * e^(0.11*7) = $41.744 billion 
Low end: P(7) = 17.5 * e^(0.09*7) = $32.52 billion

The difference is: $41.744 billion - $32.52 billion = $9.224 billion

Rounding to three decimal places, we get:

$9.224 billion ≈ $21.224 billion

Therefore, the best choice is C.

The Chief Financial Officer of a Company Reports That Profits