Answer:
28.91 years
Step-by-step explanation:
The investment value is multiplied each year by the factor ...
(1 +r/12)^12
= (1 +0.024/12)^12 = 1.002^12 ≈ 1.024265768
When the investment is multiplied by this factor for x years, the multiplication factor becomes 1.024265768^x. We want to know the value of x that makes this equal to 2:
2 = 1.024265768^x
log(2) = x·log(1.024265768) . . . . . take logarithms
x = log(2)/log(1.024265768) ≈ 28.91
It will take 28.91 years for the investment to double at 2.4% compounded monthly.
