Answer: About 16 years
Step-by-step explanation:
The formula to find the compound amount if compounded continuously is given by :-
[tex]A=Pe^{rt}[/tex], where P is Principal amount, r is the rate of interest ( in decimal) and t is time ( in years).
Given : P= $1000 ; r= 4.6%=0.046
let t be the time it will take to double the amount, the we have
[tex]2(1000)=(1000)e^{0.046\times t}[/tex]
Dividing 1000 both sides, we get
[tex]2=e^{0.046 t}[/tex]
Taking natural log on each side, we get
[tex]\ln2=\ln(0.046\times t)\\\\\Rightarrow\ 0.6931=0.046t\\\\\Rightarrow\ t=\dfrac{0.6931}{0.046}=15.0673913043\approx16\text{ years}[/tex]
Hence, it will take about 16 years to double the amount.
