55.6k views
0 votes
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.)

User Optimight
by
8.5k points

1 Answer

3 votes

Answer:


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

User Asutherland
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories