Explanation Given information: Capitalized cost is the sum of the original cost and present value of all future renewals or replacements. Annual interest rate is r and it is compounding continuously. Original cost is $ 80 , 000 and the annual renewal expense is $ 50 , 000 , spread more or less evenly over the year for a large and indefinite number of years. Explanation: The original cost is $ 80 , 000 . Since, present value = ∫ T 1 T 2 K ( t ) e − r t d t , where K ( t ) is the annual renewal expense, r is the rate of interest and T 1 to T 2 is the time interval. Therefore, an annual renewal expense = K ( t ) = $ 50 , 000 and the annual rate of interest is r . And the time period is T 1 = 0 to T 2 = ∞

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 9, Problem 58RE

To determine

The formula for the capitalized cost of the asset which involves an integral,

where capitalized cost is the sum of the original cost and the present value of all future renewals.

Original cost is $80,000 and the annual renewal expense is $50,000.

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Chapter 9, Problem 57RE

Chapter 10.1, Problem 1CYU

Chapter 9 Solutions

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The formula for the capitalized cost of the asset which involves an integral, where capitalized cost is the sum of the original cost and the present value of all future renewals. Original cost is $ 80 , 000 and the annual renewal expense is $ 50 , 000 .

Solution Summary: The author explains the formula for the capitalized cost of the asset which involves an integral.

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The formula for the capitalized cost of the asset which involves an integral,

where capitalized cost is the sum of the original cost and the present value of all future renewals.

Original cost is $80,000 and the annual renewal expense is $50,000.

Want to see the full answer?

Chapter 9 Solutions

The formula for the capitalized cost of the asset which involves an integral, where capitalized cost is the sum of the original cost and the present value of all future renewals. Original cost is $ 80 , 000 and the annual renewal expense is $ 50 , 000 .

Solution Summary: The author explains the formula for the capitalized cost of the asset which involves an integral.

Concept explainers

Videos

The formula for the capitalized cost of the asset which involves an integral, where capitalized cost is the sum of the original cost and the present value of all future renewals. Original cost is $80,000 and the annual renewal expense is $50,000.

Want to see the full answer?

Chapter 9 Solutions

The formula for the capitalized cost of the asset which involves an integral,

where capitalized cost is the sum of the original cost and the present value of all future renewals.

Original cost is $80,000 and the annual renewal expense is $50,000.