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.


It's so confusing for me now.


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