Answer:
20.4 years
Explanation:
The future value formula is ...
FV = P(1 +r/n)^(nt)
where P is the principal invested (6000), n is the number of times per year compounding occurs (12), r is the interest rate (.045), and t is the number of years.
Perhaps you're interested in a future value of $15,000 (not 1500). Then we can find t from ...
15000 = 6000(1 +.045/12)^(12t)
2.5 = 1.00375^(12t) . . . . . divide by 6000
log(2.5) = 12t·log(1.00375) . . . . . take logarithms
log(2.5)/(12log(1.00375)) = t ≈ 20.4
It will take 20.4 years for the investment to reach $15,000.