@Arthur C., my understanding is that if you own four or fewer rental units in DC (including the one you would be purchasing), you can raise the rent to anything you want.
There are a couple of things to consider here. First is that the tenant could invoke their TOPA rights making it very difficult for you to purchase the property. Assuming they don't have the funds to purchase themselves or assign their TOPA rights to someone else, you can still do it, it would just take awhile. You could also purchase their TOPA rights from them, but I wouldn't do that unless they also agreed to vacate before closing.
If you did purchase the property and raise the rent, there's a good chance you'd end up needing to evict the tenant when they couldn't and/or refused to pay the new rent. My guess is you'd be looking at $10k and 6 months for an eviction.
@John Thompson, I understand DC rent control rules a little differently, although as a DC landlord, if I'm wrong on this, I'd love different information!
My understanding is that you can raise the rent by the CPI + 2%, which for 2018-19 is a total of 3.4%. Or if the tenants are senior citizens, the lesser of CPI or Social Security COLA, which is 2.8% for 2019.
10% is the cap on what you can raise it each year (i.e. if CPI +2% or CPI/SS COLA are greater than 10%, you can only raise it 10%). I didn't think you could raise it 10% automatically. You're limited by the CPI+2 or CPI/SS COLA.
If the unit is vacant, then it's 10% (or to the same as a comparable unit up to 30%), and of course, if you're not subject to rent control, then you can raise it to whatever you want.