Answer:
<em>It will take 14 years before the investment triples</em>
Step-by-step explanation:
<u>Continuous Compounding</u>
Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.
The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:
![FV = PV\cdot e^{i.t}](https://tex.z-dn.net/?f=FV%20%3D%20PV%5Ccdot%20e%5E%7Bi.t%7D)
Where:
FV = Future value of the investment
PV = Present value of the investment
i = Interest rate
t = Time
It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.
Substituting the known values:
![3PV = PV\cdot e^{i.t}](https://tex.z-dn.net/?f=3PV%20%3D%20PV%5Ccdot%20e%5E%7Bi.t%7D)
Dividing by PV:
![3 = e^{i.t}](https://tex.z-dn.net/?f=3%20%3D%20e%5E%7Bi.t%7D)
Taking logarithms:
![\ln 3=i.t](https://tex.z-dn.net/?f=%5Cln%203%3Di.t)
Solving for t:
![\displaystyle t=\frac{\ln 3}{i}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D%5Cfrac%7B%5Cln%203%7D%7Bi%7D)
![\displaystyle t=\frac{\ln 3}{0.08}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D%5Cfrac%7B%5Cln%203%7D%7B0.08%7D)
t = 13.7 years
Rounding up:
It will take 14 years before the investment triples