P = sum of money invested (principal)

t = number of years

r = 0.082 or 8.2% is the annual interest rate

m = 4 compounding periods per year

n = m*t = 4t = 4t compounding periods

i = r/m = 0.082/4 interest rate per period

A = P + 1.5*P = 2.5P the future value

we need to find t

A = P(1 + i)^n

2.5P = P(1 + 0.082/4^(4t) divide both sides by P

(1 + 0.082/4)^(4t) = 2.5

1.0205^(4t) = 2.5

(4t) log (1.0205) = log (2.5)

t = 11.29 years

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it takes 11.29 years for the investment to increase 150%.