8 Years, 6 Months.
The formula for compound interest is
FV = P * (1 + r/n)^(tn)
where
FV = Future value
P = Initial principle
r = Annual interest rate
n = number of periods per year
t = time in years
Let's solve for t, the substitute the known value and calculate.
FV = P * (1 + r/n)^tn
FV/P = (1 + r/n)^tn
log(FV/P) = log(1 + r/n) * tn
log(FV/P)/log(1 + r/n) = tn
log(350/250)/log(1 + 0.04/12) = 12t
log(1.4)/log(1 + 0.003333333) = 12t
0.146128036/log(1.003333333) = 12t
0.146128036/0.001445241 = 12t
101.1098138 = 12t
8.425817816 = t
So it will take 8.4258 years, which is 8 years and a bit over 5 months. Rounding up, we have 8 years, 6 months.
As for the second question about how someone got 10 as an answer, all I can say is they made a mistake or that they didn't know how to calculate the correct answer.
