$($Sunk costs$)$ A young couple has made a nonrefundable deposit of the first month's rent $($equal to $$1,000)$ on a $6-$month apartment lease. The next day they find a different apartment that they like just as well. but its monthly rent is only $$900.$ They plan to be in the apartment only $6$ months. Should they switch to the new apartment? What if they plan to stay $1$ year? Assume an interest rate of $12\%$