$($Sunk costs$)$ A young couple has made a nonrefundable deposit of the first month$$s rent $($equal

to $$2,000)$ on an apartment lease for up to $2$ years. The same day later, they find a different

apartment they like just as well, but its monthly rent is only $$1,900.$ They plan to be in the

apartment for only $12$ months. Should they switch to the new apartment? What if they plan to

stay $2$ years?

Assume a nominal rate interest rate of $8\%$ convertible monthly. The rent will be paid monthly

and at the beginning of each month.