# Science:Math Exam Resources/Courses/MATH105/April 2014/Question 05 (b)

MATH105 April 2014
Other MATH105 Exams

### Question 05 (b)

An endowment is an investment account in which the balance ideally remains constant and withdrawals are made on the interest earned by the account. Such an account may be modeled by the initial value problem ${\displaystyle B'(t)=aB-m}$ for ${\displaystyle t\geq 0}$, with ${\displaystyle B(0)=B_{0}}$. The constant ${\displaystyle a}$ reflects the annual interest rate, ${\displaystyle m}$ is the annual rate of withdrawal, and ${\displaystyle B_{0}}$ is the initial balance in the account.

If ${\displaystyle a=0.02}$ and ${\displaystyle B(0)=B_{0}=\30,000}$, what is the annual withdrawal rate m that ensures a constant balance in the account?

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