# How to calculate the initial payment of a graduated payment mortgage (GPM). Real estate Mortgage analysis

My professor used this: 12%, monthly-pmt, 30-yr GPM with 4 annual step- ups of 7.5% each, then constant after year 4:

$$L=PMT \left[ PV(0.01,12,1) + \frac{1.075}{1.01^{12}}PV(0.01,12,1) + \frac{1.075^2}{1.01^{24}}PV(0.01,12,1) \\ + \frac{1.075^3}{1.01^{36}}PV(0.01,12,1) + \frac{1.075^4}{1.01^{48}}PV(0.01,312,1)\right]$$

I just don't understand why would one multiply the present value of 1\$ with the actual present value of the growth of the dollar and so forth.

Why isn't this working

$$PMT_1 = L\bigg/\left(\frac{1-((1+g)/(1+r))^N}{r-g}\right)$$

This formula is so much more logical but I'm getting something that doesn't make sense at all.

http://www.financeformulas.net/Growing-Annuity-Payment.html

It's so confusing for me now.