The napkin math (it's ugly):
Current cost per therm: .6693c
Current cost per kwh: .1301c
4 panels at 315w = 1.25kw ~= $1000
110v 1500w electric baseboard* ~= $80
Wiring,thermostat,misc ~= $120
Approx system cost $1200
Approx avg winter monthly production at my latitude 115kwh
115kwh * 3412 = 394,000 btus ~= 4 therms
Offset 4 therms per month * 6 months of the year =
.67*4*6 = $16.08 gas saved per year
1200/16.08 ~= 75 year payback.
If I substract Summer KWH - Winter KWH and estimate 75% is furnance/heating costs, I get
2.3 Kwh usage per therm usage.
2.3*4*6 *.1301 = $7.18 electric saved per year
$1200/(16.08+7.18) = 51 year payback.
*I have some old 240v baseboards, but they would quarter the output and wouldn't save that much (1100/23.26 ~= 47 year payback).
So much for that idea...