jon has $5,000 to invest in a savings account that has interest compounded annually. if he wants his money…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. Given that $P=$5000$, $A = 2\times5000=$10000$ (since the money doubles), and $t = 8$ years. Substitute these values into the formula: $10000=5000(1 + r)^8$.

Step2: Simplify the equation

Divide both sides of the equation $10000 = 5000(1 + r)^8$ by $5000$. We get $\frac{10000}{5000}=(1 + r)^8$, which simplifies to $2=(1 + r)^8$.

Step3: Solve for $r$

Take the 8th - root of both sides. $1 + r=2^{\frac{1}{8}}$. Calculate $2^{\frac{1}{8}}\approx1.0905$. Then $r=2^{\frac{1}{8}}-1\approx1.0905 - 1=0.0905$.

Step4: Convert $r$ to a percentage

To convert the decimal $r$ to a percentage, multiply by 100. So the interest rate as a percentage is $r\times100 = 9.05%$.

Answer:

$9.05%$