SOLUTION: How long would it take for an amount of money invested at an annual rate of 6% compounded semiannually, to triple?

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Question 248918: How long would it take for an amount of money invested at an annual rate of 6% compounded semiannually, to triple?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.