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:

-$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