Question

How long does it take for an investment to double its value if the interest is 7.25%

compounded continuously?

Answer 1

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.