Question 248918
future value is 3
present amount is 1
annual interest rate is 6%


6% / 2 = 3% every half a year.


interest rate equals interest rate percent divided by 100% = .03 every half a year.


the formula you need is:


3 = 1 * (1.03)^x


you need to solve for x.


formula becomes:


3 = (1.03)^x


take the log of both sides of the equation to get:


log(3) = log((1.03)^2)


by the rules of logarithms, this equation becomes:


log(3) = x*log(1.03)


divide both sides of this equation by log(1.03) to get:


x = log(3)/log(1.03)


solve for x to get:


x = 37.16700967


this means that it would take 37.16700967 half years to triple your money.


divide this by 2 to get:


18.58350483 years.


We required half years because our interest rate was every half a year (semi-annually).


these would be called semi-annual time periods.


there are 37.16700967 semi-annual time periods which equate to 18.58350483 years.