MATH105 April 2014
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Question 05 (a)
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 for , with . The constant reflects the annual interest rate, is the annual rate of withdrawal, and is the initial balance in the account.
Solve the initial value problem with and . Note that your answer depends on the constant .
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Separation of variables.
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We first solve for the differential equation:
Now we can use the initial conditions with and to find:
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