(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) = y-y² 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. Solve for the present stock of debt, y, as a function of t. What will happen to government debt as t → ∞o? Justify your response. (i) (ii)
(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) = y-y² 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. Solve for the present stock of debt, y, as a function of t. What will happen to government debt as t → ∞o? Justify your response. (i) (ii)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:(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 → o? Justify your response.
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