Explanation Given: Future value is F V ( t ) = $ 10000 for next 20 years at an interest of 2.5 % compounded continuously. Formula used: The present value of the single future payment described will be: P V = F V ( t ) ⋅ e − r t Here, P V is present value, r is rate of interest and t is time in years. Calculation: Recall the present value formula. P V = F V ( t ) ⋅ e − r t Here, P V is present value, r is rate of interest and t is time in years. The payment is to be made over 20 y e a r s , hence a definite integral is to done from t = 0 to t = 20 P V = ∫ t = 0 t = 20 F V ( t ) ⋅ e − r t d t Substitute $ 10000 for F V ( t ) , 0.025 for r and integrate. P V = ∫ t = 0 t = 20 10000 ⋅ e − 0.025 t d t Consider u for − 0.025 t , which gives following

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 13.6, Problem 34E

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To calculate: Initial amount required to fund a future income stream of FV(t)=$10000 for next 20 years at an interest of 2.5% compounded continuously.

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Chapter 13.6, Problem 33E

Chapter 13.6, Problem 35E

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MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

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Initial amount required to fund a future income stream of F V ( t ) = $ 10000 for next 20 years at an interest of 2.5 % compounded continuously.

Solution Summary: The author calculates the initial amount required to fund a future income stream of FV(t) = 157387.73.

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To calculate: Initial amount required to fund a future income stream of FV(t)=$10000 for next 20 years at an interest of 2.5% compounded continuously.

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Chapter 13 Solutions