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 .” Calculation: According to the given data f ( t ) = 15 t , r = 0.08 and T = 18 12 = 1.5 . Substitute the respective values in the present value formula and obtain P = ∫ 0 1.5 15 t e − 0.08 t d t . Substitute the respective values in the present value formula and simplify. Let u = 15 t and d v = e − 0.08 t d t . Then, d u d t = 15 ( 1 ) d u d t = 15 d u = 15 d t ∫ d v = ∫ e − 0.08 t d t v = − e − 0.08 t 0.08 Substitute the corresponding values in the above formula and simplify further. ∫ 15 t e − 0.08 t d t = 15 t ( − e − 0.08 t 0.08 ) − ∫ ( − e − 0.08 t 0.08 ) 15 d t = 15 t ( − e − 0

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

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

Publisher: Pearson Education

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Chapter 8, Problem 51RE

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To find: The present value of the money for the time period of 18 months at 8% compounded interest where the rate of money flow is f(t)=15t .

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Chapter 8, Problem 50RE

Chapter 8, Problem 52RE

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Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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The present value of the money for the time period of 18 months at 8% compounded interest where the rate of money flow is f ( t ) = 15 t .

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To find: The present value of the money for the time period of 18 months at 8% compounded interest where the rate of money flow is f(t)=15t .

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Chapter 8 Solutions