Question

Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?

Answer 1

Answer: 16 years

Step-by-step explanation:

The exponential function for continuous growth is given by :-

$P=Ae^{rt}$

, where A = initial amount, r= rate of growth and t = time.

As per given , we have

A= $2,000, =r 3.5%=0.035 and P= $3500

put these vales in equation , we get

$3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}$

Taking log on both sides , we get

$\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16$

Hence, it will take 16 years to grow to $3,500.