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Endowment model 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) = rB – m, for t ≥ 0, with B(0) = B0. The constant r > 0 reflects the annual interest rate, m > 0 is the annual rate of withdrawal, B0 is the initial balance in the account, and t is measured in years.
a. Solve the initial value problem with r = 0.05, m = $1000/year, and B0 = $15,000. Does the balance in the account increase or decrease?
b. If r = 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?
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Chapter 9 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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Thomas' Calculus: Early Transcendentals (14th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus (10th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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