How long does it take for an investment to triple in value if it is invested at 9% compounded semiannually?
(1+.09/2)^(2t) = 3
Now just solve for t (years)
110.13 years
12.5 years
To find out how long it takes for an investment to triple in value with a given interest rate and compounding period, we can make use of the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we want to find the value of 't' when A is three times the original investment amount. Let's denote the initial investment as 'P' and the tripled amount as '3P'.
We can set up the equation as follows:
3P = P(1 + 0.09/2)^(2t)
Now, we can cancel out the common factor of 'P' on both sides:
3 = (1 + 0.09/2)^(2t)
To solve for 't', we will take the logarithm of both sides. Let's use the natural logarithm (ln) for convenience:
ln(3) = ln((1 + 0.09/2)^(2t))
Using the property of logarithms, we can bring the exponent down:
ln(3) = 2t * ln(1 + 0.09/2)
Now, we can rearrange the equation and solve for 't':
t = ln(3) / (2 * ln(1 + 0.09/2))
Using a calculator, we can plug in the given values and evaluate 't'. The resulting value will represent the number of years it takes for the investment to triple in value.