To determine To find: The present value and the final amount at the rate of 3.5% compounded continuously for 4 years of the rate of money flow is $1,000 which is increasing exponentially at 5%. Explanation Formula used: Present value of money: “Present value at a time T is P = ∫ 0 T f ( t ) e − r t d t where f ( t ) is the rate of continuous money flow at an interest rate r at time t .” Accumulated amount of money flow at a time T : “Accumulated amount of money flow at a time T is A = e r T ∫ 0 T f ( t ) e − r t d t where f ( t ) is the rate of money flow at an interest rate r at time t .” Calculation: From the given information observe that f ( t ) = 1000 , r = 0.35 and T = 4 . If the rate of money flow is decreasing or increasing exponentially then f ( t ) = C e k t where C is the initial amount and k is the continuous rate of change which may positive when the rate of money flow is increasing and k is negative when the rate of money flow is decreasing. Here, C = 1000 and the continuous rate of change is increasing exponentially at 5%. Therefore, f ( t ) = 1000 e 0.05 t . Substitute the respective values and find the present value. P = ∫ 0 4 1000 e 0.05 t e − 0.035 t d t = ∫ 0 4 1000 e 0.015 t d t = 1000 [ e 0

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.3, Problem 18E

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To find: The present value and the final amount at the rate of 3.5% compounded continuously for 4 years of the rate of money flow is $1,000 which is increasing exponentially at 5%.

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Chapter 8.3, Problem 17E

Chapter 8.3, Problem 19E

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Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

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