Explanation Given: Yearly income at rate, f ( t ) = 2000. e 0.03 t dollars The rate of interest is 7 % Time period is 5 year Calculation: The income flow, future value is, At the continuous compounding annual rate, as some money invested in an account, then the balance will be the future value. The amount of money deposited is f ( t ) Time period [ 0 , T ] Annual interest rate is r The future value of income overflow will be, F V = ∫ 0 T f ( t ) e r ( T − t ) d t For, example, suppose the management expects to generate yearly income at rate of, f ( t ) = 2000. e 0.03 t dollars. The rate of interest, r = 7 % = 0.07 By substituting these values, the future value for the firm will be F V = ∫ 0 5 2000. e 0.03 t × e 0.07 ( 5 − t ) d t = 2000. e 0.03 t ∫ 0 5 e 0.04 t d t = 2000. e 0.035 [ e − 0.04 r × 1 ( − 0.04 ) ] 0 5 = 2000. e 0.035 × 1 ( − 0.04 ) [ { e − 020 } − { e 0 } ] By simplification, it would be F V = 2000 × 100 4

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.6, Problem 2PS

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Chapter 6 Solutions

Calculus

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The future value and the present value

Solution Summary: The author calculates the future value and present value of the firm by substituting these values.

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Chapter 6 Solutions