Exercise 5.3.7 A bank account is opened with $1000 at time 1 = 0 years. The account pays interest at an annual rate of 2 percent, compounded continuously; that is, the account accrues interest at a rate of 0.02p(t). Suppose the deposit rate is r(t) = 520 dollars per year from time t = 0 to time t = 2, but then drops to r(t) = 200 dollars per year for time /> 2. Formulate an appropriate ODE with an initial condition, and solve using the Laplace transform. Plot the solution for time 0

Fundamentals of Financial Management (MindTap Course List)
15th Edition
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Eugene F. Brigham, Joel F. Houston
Chapter5: Time Value Of Money
Section: Chapter Questions
Problem 27P: EFFECTIVE VERSUS NOMINAL INTEREST RATES Bank A pays 2% interest compounded annually on deposits,...
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Exercise 5.3.7 A bank account is opened with $1000 at time 1 = 0 years. The account pays interest at an annual
rate of 2 percent, compounded continuously; that is, the account accrues interest at a rate of 0.02p(t). Suppose
the deposit rate is r(t) = 520 dollars per year from time t = 0 to time t = 2, but then drops to r(t) = 200 dollars
per year for time /> 2. Formulate an appropriate ODE with an initial condition, and solve using the Laplace
transform. Plot the solution for time 0 <t<10.
Transcribed Image Text:Exercise 5.3.7 A bank account is opened with $1000 at time 1 = 0 years. The account pays interest at an annual rate of 2 percent, compounded continuously; that is, the account accrues interest at a rate of 0.02p(t). Suppose the deposit rate is r(t) = 520 dollars per year from time t = 0 to time t = 2, but then drops to r(t) = 200 dollars per year for time /> 2. Formulate an appropriate ODE with an initial condition, and solve using the Laplace transform. Plot the solution for time 0 <t<10.
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