First, determine the annual effective interest based on the annual interest and the compounding,
ieff = (1 + i/m)^m - 1
Substituting,
ieff = (1 + 0.03/12)^12 - 1 = 0.0304
To determine the future worth (F) of the current investment (P) is,
F = P(1+ieff)^n
Substituting all the known values with n unknown,
3000 = 175(1 + 0.0304)^n
Solving for n gives an n = 94.8867 years
Among the choices, the nearest value is 94.8377 years.
