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?

Question

asked Apr 1, 2021 216k views

1 Answer

Uri Shtand · Answer 1 · 2021-04-06T07:08:42+0000

Answer: 16 years

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

$3500=2000e^(0.035t)\\\\\Rightarrow\ (3500)/(2000)=e^(0.035t)\\\\\Rightarrow\ 1.75=e^(0.035t)$

Taking log on both sides , we get

$\ln 1.75=0.035t\\\\\Rightarrow\ t=(\ln1.75)/(0.035)=(0.560)/(0.035)=16$

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