(17B/19B) GPM: initial payment

[Albert Chan]

(05-30-2024 01:08 AM)Gil Wrote:  But, in your example, what is your compounding/YR, C/YR?
And what is here, for your calculation, the annual nominal interest, I%/YR?
And payments always at the end/beginning of the period?

P/Yr = C/Yr = 12 --> bank rate = APR 12% --> monthly rate i = 1%
Payment mode = END

(s-1) = APY 7.5%, converted to monthly rate s1 = 1.075^(1/12) - 1 ≈ 0.6045%

pmt1 = pmt = -468.50884659412856 (calculated from my previous post)
pmt2 = pmt * (1+s1)
pmt3 = pmt * (1+s1)^2
...
pmt60 = pmt * (1+s1)^59

Mortgage compounding and payment growth are in sync, with equivalent rate:

(q-1) = (1+s1)/(1+i) - 1 = (s1-i)/(1+i)

pmt61 = pmt * (1+s1)^60, and stay there until loan get paid off (pmt360).

(05-25-2024 08:40 PM)Albert Chan Wrote:  lua> r = -1 / c300 -- = pv6/pmt6
lua> for loops=1,5 do r = (d12*r*s - 1) / c12 end
lua> pv / r -- = pmt
-474.82512976281373

Confirm pmt (grow monthly until pmt61) without using (q-1), simply loops.

lua> i, s1
0.01    0.006044919024291704

lua> r = tvm(300,i,nil,1,0) -- = -1 / c300
lua> d1 = 1
lua> c1 = d1 + i
lua> for loops=1,60 do r = (d1*r*(1+s1)-1) / c1 end
lua> r
-128.06588485185708
lua> pv / r -- = pmt
-468.5088465941283