A young couple has made a non-refundable deposit of the first month's rent (equal to $X) on an apartment lease. The next day they find a different apartment that they like just as well, but its monthly rent is only $721. Assume an annual interest rate of r = 6%.
If they plan to be in the apartment only for 9 month. Determine the range of X in order that it pays for them to switch to the new apartment (i.e X is > what value).
(Keep your answer to 2 decimal places, e.g. 987.12.)