As MrChrister says, it all depends on the actual contract. As a general rule,
when you get PMI, you are
paying premiums for private mortgage insurance, not additional
interest, and the monthly premium stays the same (just like your
monthly mortgage payment) till the amount still owed on the mortgage
reduces to x% of the purchase price, where x is usually 80 but could be
66.67% or some other number, whatever it says in your contract.
At this point, you no longer need the PMI and the payment should stop,
but you may need to be proactive in the matter and tell them that you
have now paid off the appropriate amount of the purchase price and so
you are no longer obligated to pay the premiums for PMI. So, if you
have the money to spare, it helps to make additional payments towards
your mortgage in the early years so as to get out of paying the
PMI premiums as soon as possible.
Yes, the premiums you pay for PMI do depend on how much you put
down as a down payment, but, again, depending on the lender, there
may be broad categories for the rates, e.g. anyone putting down
less than 10% is charged the same rate regardless of whether it
was 0% down or 9.9% down while those putting down from 10% to 19.99%
are charged a smaller premium. Again, the details are specific
to the lender, and while lenders in a certain market will have similar
rates because of market competition, they can certainly differ in
the fine details.