An endowment is an investment account in which the balance ideally remains constant and withdrawals are made
Question:
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 B'(t) = aB - m for t ≥ 0, with B(0) = B0. The constant a reflects the annual interest rate, m is the annual rate of withdrawal, and B0 is the initial balance in the account.
a. Solve the initial value problem with a = 0.05, m = $1000/yr, and B0 = $15,000. Does the balance in the account increase or decrease?
b. If a = 0.05 and B0 = $50,000, what is the annual withdrawal rate m that ensures a constant balance in the account? What is the constant balance?
Step by Step Answer:
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett