When an initial amount of money, A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after t years is given by the formula: F(t) = Aert, where r is the annual interest rate earned by the account. Let A = $25,000 and r = 3.6 %. A) What is the value of the account, in dollars, after 11 years? Give your answer rounded to two decimal places. Answer $ B) What is the exact instantaneous rate of change of the value of the account at exactly 15 years? Give your answer rounded to two decimal places. dollars per year Answer: C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $1,934.09 per year? If necessary, round your answer to two decimal places. Answer: After years. D) What is the average rate of change of the future value of the account between year 11 and year 14 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.) dollars per year. (Round to two decimal places.) Answer:

When an initial amount of money, A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after t years is given by the formula: F(t) = Aert, where r is the annual interest rate earned by the account. Let A = $25,000 and r = 3.6 %. A) What is the value of the account, in dollars, after 11 years? Give your answer rounded to two decimal places. Answer $ B) What is the exact instantaneous rate of change of the value of the account at exactly 15 years? Give your answer rounded to two decimal places. dollars per year Answer: C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $1,934.09 per year? If necessary, round your answer to two decimal places. Answer: After years. D) What is the average rate of change of the future value of the account between year 11 and year 14 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.) dollars per year. (Round to two decimal places.) Answer:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose that $500 is invested at the end of every year for 5 years. The polynomial function that models the value of the investment is P(x) = 500x5 + 500x4 + 500x³ + 500x² + 500x, where x represents the effective interest rate plus 100%. One year after the last payment, the investment is worth $3200. Find the effective interest rate one year after the last payment, to the nearest tenth. (Note: You will need to subtract 1 from the value of x to find the effective interest rate.)
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