Hints:The rate of change of the stock of debt, y - is the difference between the interest owed and the fraction of the debt repaid. i.e. How much more annual repayments exceed the annual interest expenses.This is a differencial equation.i) identify the differencial equation and please show all workings (b) Given that nothing else is borrowed in the near future, the length of time it will takea government to completely eliminate its stock of debt will be entirely dependent onhow much more annual repayments exceed the annual interest expenses. Theinterest expense portion of the debt is a function of the present stock of debt, y, andis given byi(y) %3D у — у?The amount of money that the government repays to reduce its debt stock isassumed to be a fraction, a, of the present stock of debt. Repayment is done at theend of each financial year.(i)(ii)Solve for the present stock of debt, y, as a function of t.What will happen to government debt as t → ∞? Justify your response.

Here, in the question it is given that nothing else is borrowed in the near future, the length of…

Given that nothing else is borrowed in the near fut a government to completely eliminate its stock of c how much more annual repayments exceed the an interest expense portion of the debt is a function o is given by i(y) = y - y²

Given that nothing else is borrowed in the near fut a government to completely eliminate its stock of c how much more annual repayments exceed the an interest expense portion of the debt is a function o is given by i(y) = y - y²

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Hints:

The rate of change of the stock of debt, y - is the difference between the interest owed and the fraction of the debt repaid. i.e. How much more annual repayments exceed the annual interest expenses.

This is a differencial equation.

i) identify the differencial equation and please show all workings

(b) Given that nothing else is borrowed in the near future, the length of time it will take
a government to completely eliminate its stock of debt will be entirely dependent on
how much more annual repayments exceed the annual interest expenses. The
interest expense portion of the debt is a function of the present stock of debt, y, and
is given by
i(y) %3D у — у?
The amount of money that the government repays to reduce its debt stock is
assumed to be a fraction, a, of the present stock of debt. Repayment is done at the
end of each financial year.
(i)
(ii)
Solve for the present stock of debt, y, as a function of t.
What will happen to government debt as t → ∞? Justify your response.

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