Question

$800 is deposited in a bank account which is compounded continuously at 8.5% annual interest rate. The future balance of the accourby the function: A = 800e0.085t. How long will it take for the initial deposit to double? Round off to the nearest tenth of a year.

Answer 1

Given:

Function :

`A=800e^(0.085t)`

Initial deposit =$800

Annual interest rate =8.5%

`A=A_0e^(rt)`

Where,

`\begin{gathered} A=\text{Amount after t time} \\ A_0=\text{Initial amount} \\ r=\text{interest rate} \\ t=\text{time} \end{gathered}`
`\begin{gathered} r=(8.5)/(100) \\ r=0.085 \end{gathered}`

When deposit is double of initial deposit .

`\begin{gathered} 2*800=800e^(0.085t) \\ (2*800)/(800)=e^(0.085t) \\ 2=e^(0.085t) \\ \ln 2=\ln e^(0.085t) \\ 0.085t=0.69314 \\ t=(0.69314)/(0.085) \\ t=8.15 \end{gathered}`

So after 8.15 year initial amount will be double.