Answer: 9.9 years
Explanation:
We have an interest of 7.25%, compounded continuously, we can write this as:
P = A*e^(r*n)
where:
P is the total balance after n years.
A is the initial investment.
r is the ratio of increase, in the case of a continuous compound, this will be:
r = Ln(1 + 7.25%/100%) = Ln(1 + 0.0725) = 0.070
n is the time in years.
Then we want to have our initial investement doubled, this means:
P = 2*A
let's find n for this situation:
P = 2*A = A*e^(0.070*n)
2 = e^(0.070*n)
Now we can apply the Ln() to both sides, remember that:
Ln(e^x) = x
Then:
2 = e^(0.070*n)
Ln(2) = Ln(e^(0.070*n)) = 0.070*n
Ln(2)/0.070 = 9.9
So we need 9.9 years to double the initial investment.