Answer:
[tex]17.33\%[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/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
e is the mathematical constant number
we have
[tex]t=4\ years\\ A=\$20,000\\ P=\$10,000[/tex]
substitute in the formula above and solve for r
[tex]20,000=10,000(e)^{4r}[/tex]
[tex]2=(e)^{4r}[/tex]
Applying ln both sides
[tex]ln(2)=4rln(e)[/tex]
[tex]ln(2)=4r[/tex]
[tex]r=ln(2)/4=0.1733[/tex]
Convert to percentage
[tex]0.1733*100=17.33\%[/tex]
