Answer:
[tex]r=3.93\%[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=18\ years\\ P=x\\A=2x\\ r=?\\n=1[/tex]
substitute in the formula above
[tex]2x=x(1+\frac{r}{1})^{1*18}[/tex]
[tex]2=(1+r})^{18}[/tex]
Elevated both sides to 1/18
[tex]2^{\frac{1}{18}} =1+r[/tex]
[tex]r=2^{\frac{1}{18}} -1[/tex]
[tex]r=0.0393[/tex]
convert to percentage
Multiply by 100
[tex]r=3.93\%[/tex]
