Steve Simons wrote:
I changed
the rate to be 7.747975613527150% and the FV returned zero, as I'd hoped.

Wrong conclusion, IMHO.

If you want the exact rate computed by RATE(), then use =RATE(....).
FYI, the above is number is not exact either; it is merely Excel's
representation up to 15 decimal places. Of course, that is more than
good enough for most computations. But it is the "principal" of the
matter :-).

OTOH, if you would like a "nice round" interest rate like 7.75%, you
could simply compute the last payment amount, for example:

interest rate "time period
years" Payment Present Value Type
7.75% 10 -1200.00 100000.00 0

Future Value -19.18 =FV(A2/12,B2*12,C2,D2,E2)

=c2 + fv(a2/12, b2*12, c2, d2, e2)