Explanation Given information: Someone just won $72500000 in a state lottery. They paid an annuity of $ 2500000 a year for 29 years. The annual rate of inflation is r = 3 % . Formula used: Present value can be calculated as: Present value = ∫ 0 t 1 c ( t ) e − r t d t Integration by parts: ∫ u d v = u v − ∫ v d u Common integration using integration by parts ∫ x n e a x d x Where u = x n and d v = e a x d x Calculation: Consider the provided statement: The annuity paid is $ 2500000 It is provided that t 1 = 29 years and the inflation rate is r = 3 % . Now find Present value with the help of the formula: Present value = ∫ 0 t 1 c ( t ) e − r t d t Substitute the value of t 1 = 29 , r = 0

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.1, Problem 74E

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To calculate: The present value if someone just won $72500000 and it will be paid an annuity of $2500000 over the time interval of 29 years and the inflation rate is r=3%.

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Chapter 6.1, Problem 73E

Chapter 6.1, Problem 75E

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Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

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The present value if someone just won $72500000 and it will be paid an annuity of $ 2500000 over the time interval of 29 years and the inflation rate is r = 3 % .

Solution Summary: The author calculates the present value of 48420704.23 if someone won 72500000 in a state lottery.

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To calculate: The present value if someone just won $72500000 and it will be paid an annuity of $2500000 over the time interval of 29 years and the inflation rate is r=3%.

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Chapter 6 Solutions