suppose you deposit $1000 in an account paying 4.6% annual interest compounded continuously. How long will it take for the money to double?

Accepted Solution

Answer: About 16 yearsStep-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%=0.046let 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.