$(5$ points$)$ On a certain assembly line in a plant, one of the tasks is to lift a part from a conveyor and place it in a fixture for a welding process. Currently a low$-$skill laborer who costs the plant $$6,\frac{000}{?}$ month to employ $($paid at the end of each month$)$ performs this task. You are considering replacing this laborer with a robot that will cost the plant $$190,000$ to purchase and install. You estimate the salvage value of the robot to be $$11,500$ whenever the plant stops using it $($regardless of how long it is used$).$ The robot is so reliable and robust that you do not plan on having any cost for its upkeep.

$201500$

In order to help you evaluate how good this investment might be$,$ you want to determine how long it will take to "break even," $($i$.$e$.$ how long it will take for the future value of the proposed investment to be the same as the future value of employing the laborer$).$

Assuming an annual interest rate of $i=6\mathrm{.}5\%,$ compounded monthly, the amount of time it will take to "break even" is closest to:

$A=6\mathrm{.}000$

$i=\frac{6\mathrm{.}590}{12}$

$F=178500$