(17B/19B) GPM: initial payment

[Gil]

To solve PMT with growing payments we have:

PV+
{PMT×(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
PMT×[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
}=0,
with v=1/1.01, i=0.01

Then
PV+PMT×
{(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
}=0,
with v=1/1.01, i=0.01

Then
PMT=-PV /{(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5}

That's plain and easy. Trickier is to find i.