How long will it take for an investment to triple in value if it earns 11.75% compounded continuously?
It will take x years, where
e^(.1175x) = 3
To calculate the time it takes for an investment to triple in value with continuous compounding, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = Final amount (triple the initial investment)
P = Initial investment (1)
e = Euler's number, approximately 2.71828
r = Annual interest rate (11.75% or 0.1175)
t = Time (unknown)
To find the time (t), we need to rearrange the formula to solve for t:
t = ln(A/P) / r
Since we want the investment to triple, the final amount (A) will be three times the initial investment (P) or 3. Therefore, the formula becomes:
t = ln(3/1) / 0.1175
Now we can calculate the value of t by plugging the numbers into the formula:
t ≈ ln(3) / 0.1175
Using a calculator or a math software, we find that t is approximately 5.95 years.
So, it will take approximately 5.95 years for the investment to triple in value if it earns 11.75% compounded continuously.