Question

what rate of interest compounded annually is required to double an investment in 17 years?

the rate of interest required is \\(\square\\)%
(round to two decimal places as needed )

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + r)^t$, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. We want to double the investment, so $A = 2P$.

Step2: Substitute values into formula

Substitute $A = 2P$ and $t = 17$ into the formula: $2P = P(1 + r)^{17}$. Divide both sides by $P$ (since $P
eq0$) to get $2=(1 + r)^{17}$.

Step3: Solve for r

Take the 17th root of both sides: $1 + r = 2^{\frac{1}{17}}$. Calculate $2^{\frac{1}{17}}\approx1.0416$. Then subtract 1: $r\approx1.0416 - 1 = 0.0416$. Convert to percentage: $r\approx4.16\%$.

Answer:

4.16