Question

Find the time it takes for 9,400 to double when invested at an annual interest rate of 18%, compounded continuously. Find the time it takes for $940,000 to double when invested at an annual interest rate of 18%, compounded continuously.

Answer 1

`PV\text{ }\lim _(n\to\infty)(1+(r)/(n))^(nt)=e^(rt)=PVe^(rt)`
`U\sin g\text{ this new formula:}`
`9400\cdot e^(rt)=18800`
`e^(0.18t)=2`
`0.18t\text{ ln (e)= ln 2}`
`t\text{ = }(\ln 2)/(0.18)`
`t=\text{ 3.85 years}`