For the 2002 fiscal year, Lowe's Companies, Inc., reported an annual net income of $1.023 billion. Assume the income can be reinvested continuously at an annual rate of return of 9.0% compounded continuously. Also assume that Lowe's will maintain this annual net income for the next 7 years. What is the future value of its 7-year net income? Round your answer to three decimal places.

Question

Quizplus · Accepted Answer

The future value of a series of cash flows can be calculated using the formula for the future value of an annuity compounded continuously: $FV = P \times \frac{e^{rt} - 1}{r}$, where $P$ is the annual payment (net income in this case), $r$ is the annual interest rate, $t$ is the time in years, and $e$ is the base of the natural logarithm, approximately equal to 2.71828. Given $P = 1.023$ billion, $r = 0.09$, and $t = 7$, we calculate the future value of Lowe's 7-year net income. Plugging these values into the formula gives a future value, which rounds to approximately $9.976 billion, making option D the correct answer.

For the 2002 Fiscal Year, Lowe's Companies, Inc