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 information f ( t ) = 200 t 2 + 100 t + 50 , r = 0.05 % and T = 8 . Substitute the respective values and find the present value. P = ∫ 0 8 ( 200 t 2 + 100 t + 50 ) e − 0.05 t d t = 200 ∫ 0 8 t 2 e − 0.05 t d t + 100 ∫ 0 8 t e − 0.05 t d t + 50 ∫ 0 8 e − 0.05 t d t (1) Find the value of 200 ∫ 0 8 t 2 e − 0.05 t d t by column integration . D I t 2 ↘ + e − 0.05 t 2 t ↘ − e − 0.05 t − 0.05 2 ↘ + e − 0.05 t 0.0025 0 e − 0.05 t − 0.000125 200 ∫ 0 8 t 2 e − 0.05 t d t = 200 [ t 2 e − 0.05 t − 0.05 − 2 t e − 0.05 t 0.0025 + 2 e − 0.05 t − 0.000125 ] 0 8 = 200 [ − t 2 e − 0.05 t 0.05 − 2 t e − 0.05 t 0.0025 − 2 e − 0.05 t 0.000125 ] 0 8 = − 200 [ ( ( 8 ) 2 e − 0.05 ( 8 ) 0.05 + 2 ( 8 ) e − 0.05 ( 8 ) 0.0025 + 2 e − 0.05 ( 8 ) 0.000125 ) − ( ( 0 ) 2 e − 0.05 ( 0 ) 0.05 + 2 ( 0 ) e − 0.05 ( 0 ) 0.0025 + 2 e − 0.05 ( 0 ) 0.000125 ) ] = − 200 [ 64 e − 0.4 0.05 + 16 e − 0.4 0.0025 + 2 e − 0.4 0.000125 − 2 0.000125 ] ≈ 25 , 364.261975 Find the value of 100 ∫ 0 8 t e − 0.05 t d t . Let u = 100 t and d v = e − 0

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

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

Publisher: PEARSON

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Chapter 8.3, Problem 4YT

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To find: The present value of f(t)=200t2+100t+50 for 8 years at the rate of 5% compounded continuously.

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Chapter 8.3, Problem 3YT

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Chapter 8 Solutions

Calculus with Applications (11th Edition)

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 f ( t ) = 200 t 2 + 100 t + 50 for 8 years at the rate of 5% compounded continuously.

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To find: The present value of f(t)=200t2+100t+50 for 8 years at the rate of 5% compounded continuously.

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Chapter 8 Solutions