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 is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%. A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal places. Answer $44275.83 B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give your answer rounded to two decimal places. Answer: 6061.63 dollars per year C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $53,918.76 per year? If necessary, round your answer to two decimal places. Answer: After 36.25 years. D) What is the average rate of change of the future value of the account between year 9 and year 11 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.)
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 is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%. A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal places. Answer $44275.83 B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give your answer rounded to two decimal places. Answer: 6061.63 dollars per year C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $53,918.76 per year? If necessary, round your answer to two decimal places. Answer: After 36.25 years. D) What is the average rate of change of the future value of the account between year 9 and year 11 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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) = Aet, where r
is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%.
A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal
places.
Answer $44275.83
B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give
your answer rounded to two decimal places.
Answer: 6061.63
dollars per year
C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by
$53,918.76 per year? If necessary, round your answer to two decimal places.
Answer: After 36.25
Answer:
years.
D) What is the average rate of change of the future value of the account between year 9 and year 11 (i.e.
slope of the secant line connecting the points)? (Round to the nearest penny/cent.)
dollars per year. (Round to two decimal places.)
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