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

See similar textbooks

Related questions

Q: H2 AKS 17: Inflation for the housing market can be expressed by the equation i = 1 where "i" stands…

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning: "The…

Q: years öld'! 19. POPULATION GROWTH A small town in the mountains is experiencing a population boom.…

Q: The balance A (in dollars) in an investing account is given by A 7000e.0, where t is the number of…

A: According to company rule we can answer only first three sub parts and rest can be reposted.

Q: You Try: Determine the equation that would be the best fit and write the equation rounding to 2…

A: The data for the different tables are given.

Q: Statistics report that the baby mortality rate from 1971 to 1995 can be modelled through the…

A: The exponential function is represented as fx=abx, where b is the growth/decay factor. If…

Q: ents Let N(r) be the num ments required to repay an erest rate is r percent. Wha

A: It is given that Nr=$300 which is the monthly payments , loan payment is $18,000 and interest rate…

Q: tuition increased exponentially at "College A" between the years of 2009 and 2012. The tuition in…

A: Given query is to find rate of change per year and the equation for fees.

Q: 33 Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will…

A: This cane be modeled by following formula : Where, P is initial value = $ 450 r=growth rate =…

Q: 2. Congratulations! You just bought your first car, a 2003 Toyota Camry, for $4300. Your car will…

A: We know that the depreciation formula is defined as Future Value = Present Value1+r100n, here r is…

Q: 6. An investment account was opened with $3,000 in the year a) What are the independent and…

Q: The price of Michael Jordan game worn sneakers was sold for $20,000 and is represented by the…

A: Given the price of the sneakers is represented by the equation Pt…

Q: The Rule of 70 says that the time necessary for an investment to double in value is approximately…

Q: Question: Use the equation in (c) to predict the price of a 5 year - old Civic. Show your work

A: from 3rd part log(price)=βo+ log(age) given age=5 βo=1.77448

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

4. MANUFACTURING Zeller Industries bought a piece of weaving equipment for $60,000. It is expected to depreciate at an average rate of 10% per year. a. Write an equation for the value of the piece of equipment after t years. b. Find the value of the piece of equipment after 6 years.
The amount of a certain medication in a patient's body over time is given by the 500(0.93) where A represents the amount of medication t A (t) (milligrams) and t is the time (hours). How many hours will it be before the doctor must administer the medication again if it should be repeated when the level of medication in the patient decreases to 100 mg? Show your work using the Equation Editor tool. equation At Paragraph Add a File = I U A/ Record Video ▶|| O + v KY
The equation of the trend line is W = 30.94(1+0.00763)L. What is the growth rate of the trend line's equation? Express the growth rate as a percentage. Include units.
WP1: One end of a Bungee is tied to a bridge that is 120 feet above water. The other end of the Bungee is tied via padded ankle straps to a jumper's ankle. The jumper jumps and the Bungee cord extends like a rubber band and the jumper bounces up and down until coming to a halt. The Bungee cord elongation 150% of its length, meaning that the Bungee cord extended length Will be its original length plus 1.5 times of its original length. Knowing that that the jumper's height is not more 7 feet, what should the original length of the Bungee cord be to assure that the jumper under any condition stays at least 10 feet above water? Solution: Let consider the following bridge of 120 height above water.
A credit card company reported that during one decade, its average cardholder's credit card balance rose 166%. Find the average rate of change in the credit card balance from 1992 to 2002. Credit Card Debt 10,000- 8560 The average rate of change over the 10-year period was $ (Round to the nearest cent as needed.) per year. 8000- 6000- 4000- 3220 2000- -> 1992 1994 1996 1998 2000 2002 Year Print MacBook Air
The following formula is one of the formulas for the balance function for a simple interest account. B(t) = P.(1+ •t in What would be the balance in Marty's account after 43 months if he initially deposited $1,500 and his bank paid him simple interest at an annual rate of 4.98%? Round your answer to the nearest penny. Input just the number without the dollar sign. Example: 2547.32 B(43) = $[B]