Use the formula for compounding interest:
FV = PV(1+r/n)^{ny} where:
- FV = Future Value
- PV = Present Value
- r = annual interest rate in decimal form
- n = Compounding terms per year
- y = years
For your particular problem we have:
- FV = 3 (because the current value is being tripled)
- PV = 1 (because no specific PV was given you can use 1)
- r = 0.054
- n = 1 (because it is compounded annually, or once a year)
- y = to be determined
Putting your information into the formula gives:
- 3=1(1+.054/1)^{1y} , we can simplify this by getting rid of the 1 coefficients
- 3 = (1.054)^{y}
We will have to apply the ln function to both sides in order to solve for y
- ln(3) = ln(1.054)^{y}
- ln(3) = y ln(1.054) .... using the property of logarithms ln(A^{B}) = B ln(A)
- this gives us y = ln(3) / ln(1.054) = 20.889 which is about 21 years
So, it will take approximately 21 years for a certain investment to triple itself if it earns 5.4% interest compounded annually.
Hope this was helpful.
Please leave a comment if it was (or wasn't) helpful for you.
David