Answer:
Should they switch to the new apartment? If they plan to stay 6 months.
No, since the difference in rent is too small and it is simply not worth it.
If they were planning to saty in teh new apartment for 1 year, they would need to find the epresent value of the difference between one apartment and the other = $100 x 11.255 (PVIFA, 1%, 12 peridos) = $1,125.50. This amount is higher than the initial deposit, so they should choose the other apartment.