Finding the monthly payment for fixed-rate mortgage, but with first month interest free. I'm trying to calculate the monthly payment of a fixed-rate (annuity) loan, but with the twist that the first month is interest free.
I.e., I have a principal $P_0$ - the total sum that I've loaned - and I want to pay it off completely in $N$ months.  The monthly interest rate is $r$, except for the first month, where it is zero. 
I want to find the annuity $c$. The formula I've found helps me calculate this in the situation without the first month exception:
$$c = \frac{r}{1 - (1+r)^{-N}}P_0$$
How can I modify it?

My friend helped me come up with this solution:
$$c = \frac{P_0  (1+r)^{N-1}r}{(1+r)^N-1} $$
