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5 August, 08:02

The initial cost of a packed-bed degassing reactor for removing trihalomethanes from potable water is $84,000. The annual operating cost for power, site maintenance, etc. is $13,000. If the salvage value of the pumps, blowers, and control systems is expected to be $9,000 at the end of 10 years, the AW of the packed-bed reactor, at an interest rate of 8% per year, is closest to:

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  1. 5 August, 09:13
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    -$24,900

    Explanation:

    Solution

    Given:

    The annual payment is defined as:

    A = F [i / (1 + i) ^n - 1

    Where,

    F = The sum of amount accumulated

    i = The interest rate (annual)

    n = the number of years

    The standard notation equation becomes this

    =A = F (A/F, i, n)

    Now,

    The annual payment is A = P [ i (1 + i) ^n / (1 + i) ^n - 1

    where

    P = The present value,

    i = The interest rate (annual)

    n = the number of year

    The standard notation equation becomes this

    =A = P (A/P, i, n)

    We recall that,

    The first cost P is $84,000.

    Now,

    A = $13,000, S = $9,000, n = 10 years, and i = 8 %

    Thus,

    AW = - 84000 (A / P 8% 10) - 13000 + 9000 (A/F, 8%, 10)

    =-84000 (0.149) - 13000 + 9000 (0.069)

    = - $24,900
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