(a) 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 .” Integration by parts: “If u and v are differentiable functions, then ∫ u d v = u v − ∫ v d u .” Calculation: According to the given data f ( t ) = 0.05 t + 500 , r = 0.08 and T = 10 . Substitute the respective values in the present value formula. P = ∫ 0 10 ( 0.05 t + 500 ) e − 0.08 t d t P = ∫ 0 10 0.05 t e − 0.08 t d t + ∫ 0 10 500 e − 0.08 t d t (1) Solve the integral ∫ 0 10 0.05 t e − 0.08 t d t . Let u = 0.05 t and d v = e − 0.08 t d t . Then, d u d t = 0.05 ( 1 ) d u d t = 0.05 d u = 0.05 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. ∫ 0.05 t e − 0.08 t d t = 0.05 t ( − e − 0.08 t 0.08 ) − ∫ ( − e − 0.08 t 0.08 ) ( 0.05 ) d t = 0.05 t ( − e − 0.08 t 0.08 ) + 0 (b) To determine To find: The accumulated amount of money flow at t = 10 if f ( t ) = 0.05 t + 500 f ( t ) = 0.05 t + 500 , r = 8 % and T = 10 .

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

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

Publisher: PEARSON

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Chapter 16.3, Problem 12E

(a)

To determine

To find: The present value of the money for the time period of 10 years at 8% compounded interest where the rate of money flow is f(t)=0.05t+500 .

(b)

To determine

To find: The accumulated amount of money flow at t = 10 if f(t)=0.05t+500 f(t)=0.05t+500 , r=8% and T=10 .

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Chapter 16.3, Problem 11E

Chapter 16.3, Problem 13E

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Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 16.1 - Find xe2xdx.Ch. 16.1 - Find ln2xdx.Ch. 16.1 - Prob. 3YT Ch. 16.1 - Find 1ex2lnxdx.Ch. 16.1 - Prob. 5YT Ch. 16.1 - Prob. 1WE Ch. 16.1 - Find the following. W2.(3x52x3)dx Ch. 16.1 - Find the following. W3.(x23+1x)dx Ch. 16.1 - Prob. 4WE Ch. 16.1 - Use integration by parts to find the integrals in...

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The present value of the money for the time period of 10 years at 8% compounded interest where the rate of money flow is f ( t ) = 0.05 t + 500 .

Solution Summary: The author explains the present value of money for the time period of 10 years at 8% compounded interest.