A young couple has made a deposit of the first month's rent (equal to $1,000) on a 6-month apartment lease. The deposit is refundable at the end of six months if they stay until the end of the lease. The next day they find a different apartment that they like just as well, but its monthly rent is only $900. And they would again have to put a deposit of $900 refundable at the end of 6 months.
They plan to be in the apartment only 6 months. Should they switch to the new apartment? Assume an (admittedly unrealistic!) interest rate of 12% per month compounded monthly. Please show steps how you get an answer and please be clear in your explanation.