Chapter 8.8, Problem 77E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Capitalized Cost In Exercises 77 and 78, find the capitalized cost C of an asset (a) for n = 5 years, (b) for n = 10 years, and (c) forever. The capitalized cost is given by C = C 0 + ∫ 0 n c ( t ) e − r t   d t where C 0 is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and c ( t ) is the annual cost of maintenance.C0 = $700,000c(t) =$ 25,000r = 0.06

(a)

To determine

To calculate: The capitalized cost C of an asset for 5 years where C=C0+0nc(t)ertdt

Explanation

Given:

The capitalized cost is:

C=C0+âˆ«0nc(t)eâˆ’rtdt

Where n is the number of years, C0 is the original investment, t is time and c(t) is the annual cost of maintenance.

And

C0=$700,000c(t)=$25,000r=0.06

Formula used:

Use the formula:

âˆ«eax=1aeax

Calculation:

Consider

(b)

To determine

To calculate: The capitalized cost C of an asset for 10 years where C=C0+0nc(t)ertdt

(c)

To determine

To calculate: The capitalized cost C of an asset for infinite years C=C0+0nc(t)ertdt

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