Question

Suppose that Mark deposits $4,000 per year into an account that has a 5.5% annual interest rate compounded continuously. Assume a continuous money flow, then it takes years for the account to be worth $200,000. (Round the answer to an integer at the last step.)

Answer 1

`t=24yrs`

Explanation:

From the question we are told that:

Principle
`P=\$4000`

Interest
`r=5.5\%`

Final Value
`X=\$200000`

Generally the equation Time is mathematically given by

`X=P *e^(r*t)\int^t_0 e^(r*t) dt`

`200000=4000 *e^(0.055*t)\int^t_0 e^(0.055*t) dt`

`200000=4000* (e^(0.055*t)-1)/(0.055)`

`e^(0.055*t)=(15)/(4)`

`e^(0.055*t)=3.75`

`0.055t=ln3.75`

`t=24.03`

Therefore the number of years it takes years for the account to be worth $200,000.

`t=24yrs`