Answer:
x = 7.5
Step-by-step explanation:
To find the annual interest rate (x%), we can use the compound interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
In this case:
Substitute the given values into the formula:
[tex]28712.59=20000\left(1+\dfrac{r}{1}\right)^{1 \times 5}[/tex]
[tex]28712.59=20000\left(1+r\right)^{5}[/tex]
Divide both sides of the equation by 20000:
[tex]\dfrac{28712.59}{20000}=\left(1+r\right)^{5}[/tex]
Now, take the fifth root of both sides:
[tex]\sqrt[5]{\dfrac{28712.59}{20000}}=1+r[/tex]
Subtract 1 from both sides:
[tex]r=\sqrt[5]{\dfrac{28712.59}{20000}}-1[/tex]
Compute the value of r:
[tex]r=0.0750000260...[/tex]
To convert into a percentage, multiply r by 100:
[tex]r = 7.500000260...\%[/tex]
[tex]r = 7.5\%\;(\sf nearest\;tenth)[/tex]
So, the annual interest rate (x%) is approximately 7.5%, which means the value of x is 7.5.
