FINITE MATHEMATICS & ITS APPLICATIONS
12th Edition
ISBN: 9781323788707
Author: Goldstein
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 10.5, Problem 18E
(a)
To determine
To calculate: The first five values generated by different equation
(b)
To determine
To calculate: the solution of the difference equation
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
12
15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
Assignment 3 graph.docx
Score: 1 out of 1
Comment:
(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs (in thousands of…
Use the method of undetermined coefficients to solve the given nonhomogeneous system.
dx
dt
=
2x + 3y − 8
dy
dt
=
−x − 2y + 6
X(t) =
As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk.
(a)
Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%.
Assume
that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let
ds ≥ R − Rs
with
ds ≥ 0.
Then make the objective function:
Min
1
5
5
s = 1
ds2.
Let
FS = proportion of portfolio invested in the foreign stock mutual fund
IB = proportion of portfolio invested in the intermediate-term bond fund
LG = proportion of portfolio invested in the large-cap growth fund
LV = proportion of portfolio invested in the large-cap value fund…
Chapter 10 Solutions
FINITE MATHEMATICS & ITS APPLICATIONS
Ch. 10.1 - Solution can be found following the section...Ch. 10.1 - Solution can be found following the section...Ch. 10.1 - Calculate the future amount of $2000 after 6...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 16, given the values of i and n under...Ch. 10.1 - In Exercises 16, given the values of i and n under...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 712, given the values of i, n, P, and...
Ch. 10.1 - In Exercises 712, given the values of i, n, P, and...Ch. 10.1 - In Exercises 7–12, given the values of i, n, P,...Ch. 10.1 - In Exercises 7–12, given the values of i, n, P,...Ch. 10.1 - Prob. 11ECh. 10.1 - In Exercises 712, given the values of i, n, P, and...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 13–38, solve each problem.
16. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - Prob. 18ECh. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Present...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Comparing...Ch. 10.1 - In Exercises 1338, solve each problem. Comparing...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - Prob. 27ECh. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - Prob. 29ECh. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Interest...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 3952 concern simple interest. Future...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 3952 concern simple interest. Present...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Present...Ch. 10.1 - Exercises 39–52 concern simple interest.
52. Time...Ch. 10.1 - Future Value Compute the future value after 1 year...Ch. 10.1 - Future Value Compute the future value after 1 year...Ch. 10.1 - Effective Rate of Interest In Exercises 5558,...Ch. 10.1 - Effective Rate of Interest In Exercises 5558,...Ch. 10.1 - Effective Rate of Interest In Exercises 55–58,...Ch. 10.1 - Effective Rate of Interest In Exercises 55–58,...Ch. 10.1 - Prob. 59ECh. 10.1 - Savings Account During the 1990s, a deposit was...Ch. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Doubling Time(True or False) An investment growing...Ch. 10.1 - Prob. 65ECh. 10.1 - Future Value If your stock portfolio gained 20% in...Ch. 10.1 - 67. Comparing Investments The same amount of money...Ch. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - 76. Savings Account Ten thousand dollars is...Ch. 10.1 - Prob. 77ECh. 10.1 - Prob. 78ECh. 10.1 - Comparing Investments Consider the following two...Ch. 10.1 - 80. Comparing Investments Consider the following...Ch. 10.2 - Solutions can be found the section exercises....Ch. 10.2 - Prob. 2CYUCh. 10.2 - Prob. 3CYUCh. 10.2 - Exercises 1 and 2 describe increasing annuities....Ch. 10.2 - Exercises 1 and 2 describe increasing annuities....Ch. 10.2 - Exercises 3 and 4 describe decreasing annuities....Ch. 10.2 - Exercises 3 and 4 describe decreasing annuities....Ch. 10.2 - In Exercises 5 and 6, calculate the future value...Ch. 10.2 - In Exercises 5 and 6, calculate the future value...Ch. 10.2 - In Exercises 7 and 8, calculate the rent of the...Ch. 10.2 - In Exercises 7 and 8, calculate the rent of the...Ch. 10.2 - In Exercises 9 and 10, calculate the present value...Ch. 10.2 - In Exercises 9 and 10, calculate the present value...Ch. 10.2 - In Exercises 11 and 12, calculate the rent of the...Ch. 10.2 - In Exercises 11 and 12, calculate the rent of the...Ch. 10.2 - Savings Account Ethan deposits $500 into a savings...Ch. 10.2 - Savings Account Emma deposits $2000 into a savings...Ch. 10.2 - Prob. 15ECh. 10.2 - Savings Account A person deposits$5000 into a...Ch. 10.2 - In Exercises 17–20, determine the amount of...Ch. 10.2 - In Exercises 1720, determine the amount of...Ch. 10.2 - In Exercises 1720, determine the amount of...Ch. 10.2 - Prob. 20ECh. 10.2 - Comparing Payouts Is it more profitable to receive...Ch. 10.2 - Comparing Payouts Is it more profitable to receive...Ch. 10.2 - Comparing Bonus Plans When Bridget takes a new...Ch. 10.2 - Comparing Lottery Payouts A lottery winner is...Ch. 10.2 - College Allowance During Jacks first year at...Ch. 10.2 - Magazine Subscription Suppose that a magazine...Ch. 10.2 - 27. Savings Account Suppose that $1000 was...Ch. 10.2 - Savings Account Suppose that you opened a savings...Ch. 10.2 - 29. Savings Account Ms. Jones deposited $100 at...Ch. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Savings Account How much money must you deposit...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Municipal Bond A municipal bond pays 4% interest...Ch. 10.2 - Present Value What is the present value of a loan...Ch. 10.2 - 37. Business Loan A business loan for $200,000...Ch. 10.2 - 38. Lottery Payoff A lottery winner is to receive...Ch. 10.2 - Prob. 39ECh. 10.2 - A sinking fund is an increasing annuity set up by...Ch. 10.2 - Prob. 41ECh. 10.2 - A sinking fund is an increasing annuity set up by...Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - A deferred annuity is a type of decreasing annuity...Ch. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - In Exercises 51–58, give the settings or...Ch. 10.2 - Prob. 59ECh. 10.2 - 60. Time Interval A person deposits $800 at the...Ch. 10.2 - Prob. 61ECh. 10.2 - Home Repairs Fund Bob needs $3064 to have some...Ch. 10.2 - Prob. 63ECh. 10.3 - Solution can be found following the section...Ch. 10.3 - Solution can be found following the section...Ch. 10.3 - Solution can be found following the section...Ch. 10.3 - 1. Loan Payment A car loan of $10,000 is to be...Ch. 10.3 - Loan Payment A loan of $5000 is to be repaid with...Ch. 10.3 - Loan Payment A loan of $4000 is to be repaid with...Ch. 10.3 - Loan Payment A loan of $3000 is to be repaid with...Ch. 10.3 - Loan Amount The weekly payment on a 2-year loan at...Ch. 10.3 - Loan Amount The quarterly payment on a 5-year loan...Ch. 10.3 - Mortgage Payment Find the monthly payment on a...Ch. 10.3 - 8. Mortgage Payment Find the monthly payment on a...Ch. 10.3 - 9. Mortgage Amount Find the amount of a 30-year...Ch. 10.3 - Mortgage Amount Find the amount of a 25-year...Ch. 10.3 - Mortgage Balance A 30-year mortgage at 4.2%...Ch. 10.3 - 12. Mortgage Balance A 25-year mortgage at 4.5%...Ch. 10.3 - 13. Loan Interest A loan with a weekly payment of...Ch. 10.3 - Loan Interest A loan with a quarterly payment of...Ch. 10.3 - Amortization Schedule Write out a complete...Ch. 10.3 - Amortization Schedule Write out a complete...Ch. 10.3 - 17. Mortgage Consider a $204,700, 30-year mortgage...Ch. 10.3 - 18. Mortgage James buys a house for $370,000. He...Ch. 10.3 - 19. Car Loan Susie takes out a car loan for $9480...Ch. 10.3 - Loan Consider a $21,281.27 loan for 7 years at 8%...Ch. 10.3 - Prob. 21ECh. 10.3 - Comparing Financing Options In a recent year, Ford...Ch. 10.3 - 23. Comparing Financing Options A bank makes the...Ch. 10.3 - Buy Now or Later? According to an article in the...Ch. 10.3 - Balloon Payment A loan is to be amortized over an...Ch. 10.3 - 26. Balloon Payment A loan of $127,000.50 is to be...Ch. 10.3 - 27. Car Loan A car is purchased for $6287.10, with...Ch. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Terminating a Mortgage In 2006, Emma purchased a...Ch. 10.3 - Refinancing a Mortgage A real estate speculator...Ch. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Total of Loan Payment Suppose that you borrow...Ch. 10.3 - 36. Loan Amount Suppose that you borrow money at...Ch. 10.3 - Let Bn= balance of a loan after n payments, In=...Ch. 10.3 - Let QnandIn be as defined in Exercise 37. a. Use...Ch. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - In Exercises 39–46, give settings or statements to...Ch. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Debt Reduction A loan of $10,000 at 9% interest...Ch. 10.3 - 50. Debt Reduction A loan of $4000 at 6% interest...Ch. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.4 - Solution can be found following the section...Ch. 10.4 - Prob. 2CYUCh. 10.4 - Prob. 3CYUCh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Comparing IRAs Rework Examples 1 and 3 for the...Ch. 10.4 - Roth IRA Rework Exercise 5 for a Roth IRA.Ch. 10.4 - 8. Comparing IRAs Rework Examples 1 and 3 for the...Ch. 10.4 - Value of Starting an IRA Early Redo Example 4...Ch. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - 26. True or False Refer to Example 10. If the...Ch. 10.4 - Prob. 27ECh. 10.4 - APR In multiple-choice Exercises 2730, assume that...Ch. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Effective Mortgage Rate In multiple-choice...Ch. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Interest-Only Mortgage Consider a 15-year mortgage...Ch. 10.4 - 42. Interest-Only Mortgage Consider a 15-year...Ch. 10.4 - 43. Adjustable-Rate Mortgage Consider a 25-year...Ch. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.5 - Solution can be found following the section...Ch. 10.5 - Prob. 2CYUCh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - In Exercises 1–10, give a difference equation for...Ch. 10.5 - In Exercises 1–10, give a difference equation for...Ch. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - In Exercises 11 and 12, answer the questions....Ch. 10.5 - In Exercises 11 and 12, answer the questions....Ch. 10.5 - Prob. 13ECh. 10.5 - In Exercises 1318, (a) determine the first five...Ch. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - In Exercises 1938, use difference equations to...Ch. 10.5 - In Exercises 1938, use difference equations to...Ch. 10.5 - In Exercises 19–38, use difference equations to...Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Elevation and Atmospheric Pressure The atmospheric...Ch. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 50ECh. 10 - 1. What is meant by principal?
Ch. 10 - Prob. 2FCCECh. 10 - 3. What is meant by the balance in a savings...Ch. 10 - Prob. 4FCCECh. 10 - Prob. 5FCCECh. 10 - Prob. 6FCCECh. 10 - Prob. 7FCCECh. 10 - 8. Explain the difference between the nominal and...Ch. 10 - Prob. 9FCCECh. 10 - Prob. 10FCCECh. 10 - Prob. 11FCCECh. 10 - Prob. 12FCCECh. 10 - Prob. 13FCCECh. 10 - Prob. 14FCCECh. 10 - Prob. 15FCCECh. 10 - Prob. 16FCCECh. 10 - Prob. 17FCCECh. 10 - Prob. 18FCCECh. 10 - How are finance charges on a consumer loan...Ch. 10 - Prob. 20FCCECh. 10 - Prob. 21FCCECh. 10 - Prob. 22FCCECh. 10 - Prob. 23FCCECh. 10 - Prob. 24FCCECh. 10 - Prob. 25FCCECh. 10 - Prob. 26FCCECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Nonstandard Mortgage A real estate investor takes...Ch. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Interest-Only Mortgage Consider a 25-year mortgage...Ch. 10 - 36. Adjustable-Rate Mortgage Consider a 25-year...Ch. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Suppose that a $100,000 investment grows 3% during...Ch. 10 - Prob. 2PCh. 10 - 3. Consider an annuity in which $100,000 is...Ch. 10 - Rework Exercise 3, where the interest rate is 4%...Ch. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - 7. Show that, if an investment of P dollars earns ...Ch. 10 - 8. Which of the following two statements is true?...Ch. 10 - Show that, if $1000 is invested at 8% interest...Ch. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - Prob. 12PCh. 10 - Prob. 13PCh. 10 - Prob. 14PCh. 10 - Prob. 15P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Calculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forwardFor each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
- Problem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forward
- Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forward
- The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward3. Consider the polynomial equation 6-iz+7z2-iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forwardWrite the equation of the trigonometric function shown in the graph. LO 5 4 3 2 1 y -5 -5 4 8 8 500 -1 -2 -3 -4 -5 x 5 15л 5л 25л 15л 35π 5л 4 8 2 8 4 8arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY