Question

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

Answer 1

Answer: About 16 years

Step-by-step explanation:

The formula to find the compound amount if compounded continuously is given by :-

$A=Pe^{rt}$, 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

$2(1000)=(1000)e^{0.046\times t}$

Dividing 1000 both sides, we get

$2=e^{0.046 t}$

Taking natural log on each side, we get

$\ln2=\ln(0.046\times t)\\\\\Rightarrow\ 0.6931=0.046t\\\\\Rightarrow\ t=\dfrac{0.6931}{0.046}=15.0673913043\approx16\text{ years}$

Hence, it will take about 16 years to double the amount.