Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 13.1, Problem 36E
Finding the Present Value of a Compound Interest Retirement Account Tanja wants to establish an account that will supplement her retirement income beginning 30 years from now. For each interest rate, find the lump sum she must deposit today so that $750,000 will be available at time of retirement.
6% compounded quarterly
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4. Assume that a risk-free money market account is added to the market described in Q3.
The continuously compounded rate of return on the money market account is log (1.1).
(i) For each given μ, use Lagrange multipliers to determine the proportions (as a
function of μ) of wealth invested in the three assets available for the minimum
variance portfolio with expected return μ.
(ii) Determine the market portfolio in this market and calculate its Sharp ratio.
3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free
asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05,
Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75.
(i) Given that an investor is targeting a total expected return of μ = 0.2. What
portfolio weights should they choose to meet this goal with minimum portfolio
variance? Correct all your calculations up to 4 decimal points.
(ii) Determine the global minimum-variance portfolio and the expected return and
variance of return of this portfolio (4 d.p.).
(iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient
frontier.
(iv) Without further calculation, explain how the minimum variance of the investor's
portfolio return will change if the two risky assets were independent.
2. A landlord is about to write a rental contract for a tenant which lasts T months. The
landlord first decides the length T > 0 (need not be an integer) of the contract, the
tenant then signs it and pays an initial handling fee of £100 before moving in. The
landlord collects the total amount of rent erT at the end of the contract at a continuously
compounded rate r> 0, but the contract stipulates that the tenant may leave before T,
in which case the landlord only collects the total rent up until the tenant's departure
time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r.
(i) Calculate the expected total payment EW the landlord will receive in terms of T.
(ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides
that the rental rate r should depend on the contract length T by
r(T)
=
λ
√T
1
For each given λ, what T (as a function of X) should the landlord choose so as to
maximise their expected utility? Justify your answer.
Hint. It might be…
Chapter 13 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - In the following exercises, assume whenever...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...Ch. 13.1 - Find the future value of each deposit if the...
Ch. 13.1 - Solve each interest-related problem.
11. Simple...Ch. 13.1 - Solve each interest-related problem. Simple...Ch. 13.1 - Solve each interest-related problem.
13. Simple...Ch. 13.1 - Solve each interest-related problem.
14. Simple...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - Find the missing final amount (future value)...Ch. 13.1 - For each deposit, find the future value (that is,...Ch. 13.1 - For each deposit, find the future value (that is,...Ch. 13.1 - For each deposit, find the future value (that is,...Ch. 13.1 - For each deposit, find the future value (that is,...Ch. 13.1 - Occasionally a savings account may actually pay...Ch. 13.1 - Occasionally a savings account may actually pay...Ch. 13.1 - Occasionally a savings account may actually pay...Ch. 13.1 - Solve each interest-related problem. Finding the...Ch. 13.1 - Solve each interest-related problem. Finding the...Ch. 13.1 - Solve each interest-related problem. In the...Ch. 13.1 - Find the present value for each future amount....Ch. 13.1 - Find the present value for each future amount....Ch. 13.1 - Prob. 33ECh. 13.1 - Find the present value for each future amount.
34....Ch. 13.1 - Finding the Present Value of a Compound Interest...Ch. 13.1 - Finding the Present Value of a Compound Interest...Ch. 13.1 - Finding the Present Value of a Compound Interest...Ch. 13.1 - Finding the Present Value of a Compound Interest...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Finding the Effective Annual Yield in a Savings...Ch. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.1 - Prob. 50ECh. 13.1 - Prob. 51ECh. 13.1 - Prob. 52ECh. 13.1 - Comparing Bank Savings Rates Bank A pays a nominal...Ch. 13.1 - Prob. 54ECh. 13.1 - Prob. 55ECh. 13.1 - Prob. 56ECh. 13.1 - Prob. 57ECh. 13.1 - Estimating the Inflation Rate by the Rule of 70...Ch. 13.1 - Estimating the Inflation Rate by the Rule of 70...Ch. 13.1 - Estimating the Inflation Rate by the Rule of 70...Ch. 13.1 - Estimating the Inflation Rate by the Rule of 70...Ch. 13.1 - Prob. 62ECh. 13.1 - Prob. 63ECh. 13.1 - Prob. 64ECh. 13.1 - Estimating Future Prices for Constant Annual...Ch. 13.1 - Estimating Future Prices for Constant Annual...Ch. 13.1 - Item Price Year Purchased Price in 2013
Evening...Ch. 13.1 - Estimating Future Prices for Variable Annual...Ch. 13.1 - Estimating Future Prices for Variable Annual...Ch. 13.1 - Estimating Future Prices for Variable Annual...Ch. 13.1 - Prob. 71ECh. 13.1 - Prob. 72ECh. 13.2 - Round all monetary answers to the nearest cent...Ch. 13.2 - Round all monetary answers to the nearest cent...Ch. 13.2 - Round all monetary answers to the nearest cent...Ch. 13.2 - Round all monetary answers to the nearest cent...Ch. 13.2 - Round all monetary answers to the nearest cent...Ch. 13.2 - Financing a New Car Purchase Suppose you want to...Ch. 13.2 - Financing a New Car Purchase Suppose you want to...Ch. 13.2 - Financing a New Car Purchase Suppose you want to...Ch. 13.2 - Financing a New Car Purchase Suppose you want to...Ch. 13.2 - Financing a New Car Purchase Suppose you want to...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - In Exercises 11-16, use the add-on method of...Ch. 13.2 - Work each problem.
17. Finding the Monthly Payment...Ch. 13.2 - Work each problem. Finding the Monthly Payment for...Ch. 13.2 - Work each problem.
19. Finding the Monthly Payment...Ch. 13.2 - Work each problem.
20. Finding the Monthly Payment...Ch. 13.2 - Work each problem.
21. Finding the Amount Borrowed...Ch. 13.2 - Work each problem.
22. Finding an Add-On Interest...Ch. 13.2 - Work each problem. Finding the Term of an Add-On...Ch. 13.2 - Work each problem.
24. Finding the Number of...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges Find the finance charge...Ch. 13.2 - Finding Finance Charges and Account Balances Using...Ch. 13.2 - Finding Finance Charges and Account Balances Using...Ch. 13.2 - Finding Finance Charges and Account Balances Using...Ch. 13.2 - Finding Finance Charges and Account Balances Using...Ch. 13.2 - Finding Finance Charges In Exercises 35 and 36,...Ch. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Prob. 41ECh. 13.2 - Prob. 42ECh. 13.2 - Prob. 43ECh. 13.2 - Write out your response to each of the...Ch. 13.2 - Prob. 45ECh. 13.2 - Prob. 46ECh. 13.2 - Prob. 47ECh. 13.2 - Recall a car-buying experience you have had, or...Ch. 13.2 - Prob. 49ECh. 13.2 - Comparing Bank Card Accounts Ruby is considering...Ch. 13.3 - Round all monetary answers to the nearest cent...Ch. 13.3 - Round all monetary answers to the nearest cent...Ch. 13.3 - Round all monetary answers to the nearest cent...Ch. 13.3 - Round all monetary answers to the nearest cent...Ch. 13.3 - Finding the Monthly PaymentFind the monthly...Ch. 13.3 - Finding the Monthly PaymentFind the monthly...Ch. 13.3 - Finding the Monthly Payment Find the monthly...Ch. 13.3 - Finding the Monthly Payment Find the monthly...Ch. 13.3 - Finding True Annual Interest Rate Find the APR...Ch. 13.3 - Finding True Annual Interest Rate Find the APR...Ch. 13.3 - Finding True Annual Interest Rate Find the APR...Ch. 13.3 - Finding True Annual Interest Rate Find the APR...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Finding Finance Charge and True Annual Interest...Ch. 13.3 - Finding Finance Charge and True Annual Interest...Ch. 13.3 - Finding Finance Charge and True Annual Interest...Ch. 13.3 - Finding Finance Charge and True Annual Interest...Ch. 13.3 - Comparing the Actuarial Method and the Rule of 78...Ch. 13.3 - Comparing the Actuarial Method and the Rule of 78...Ch. 13.3 - Comparing the Actuarial Method and the Rule of 78...Ch. 13.3 - Comparing the Actuarial Method and the Rule of 78...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Unearned Interest by the Actuarial Method Each...Ch. 13.3 - Comparing Loan Choices Phan needs to borrow $5000...Ch. 13.3 - Comparing Loan Choices Phan needs to borrow $5000...Ch. 13.3 - Comparing Loan Choices Phan needs to borrow $5000...Ch. 13.3 - Comparing Loan Choices Phan needs to borrow $5000...Ch. 13.3 - Comparing Loan Choices Phan needs to borrow $5000...Ch. 13.3 - 32.Describe why, in Example 1, the APR and the...Ch. 13.3 - Approximating the APR of an Add-On Rate To convert...Ch. 13.3 - Approximating the APR of an Add-On Rate To convert...Ch. 13.3 - The Rule of 78 with Prepayment Penalty A certain...Ch. 13.3 - The Rule of 78 with Prepayment Penalty A certain...Ch. 13.3 - The Rule of 78 with Prepayment Penalty A certain...Ch. 13.3 - The Rule of 78 with Prepayment Penalty A certain...Ch. 13.3 - Write out your response to each exercise.
39. Why...Ch. 13.3 - Prob. 40ECh. 13.3 - Prob. 41ECh. 13.3 - Write out your response to each exercise.
42....Ch. 13.3 - Write out your response to each exercise. Find the...Ch. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Monthly Payment on a Fixed-Rate Mortgage Find the...Ch. 13.4 - Amortization of a Fixed-Rate Mortgage Complete the...Ch. 13.4 - Amortization of a Fixed-Rate Mortgage Complete the...Ch. 13.4 - Mortgage: $143,200 Amortization Schedule Interest...Ch. 13.4 - Mortgage: $124,750 Amortization...Ch. 13.4 - Prob. 13ECh. 13.4 - Mortgage: $150,000 Interest rate: 4.25% Term of...Ch. 13.4 - Finding Monthly Mortgage Payments Find the total...Ch. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Finding Monthly Mortgage Payment Find the total...Ch. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Comparing Total Principal and Interest on a...Ch. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.4 - Prob. 32ECh. 13.4 - Long-Term Effect of Interest Rates You may...Ch. 13.4 - Prob. 34ECh. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - The Effect of the Term on Total Amount Paid...Ch. 13.4 - The Effect of the Term on Total Amount Paid...Ch. 13.4 - Prob. 39ECh. 13.4 - Prob. 40ECh. 13.4 - Prob. 41ECh. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - The Effect of Rate Caps on Adjustable-Rate...Ch. 13.4 - Prob. 45ECh. 13.4 - Prob. 46ECh. 13.4 - Prob. 47ECh. 13.4 - Prob. 48ECh. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - Prob. 51ECh. 13.4 - Prob. 52ECh. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.4 - Prob. 55ECh. 13.4 - Exercises 55 and 56 refer to the When Will I Ever...Ch. 13.4 - Prob. 57ECh. 13.4 - Prob. 58ECh. 13.4 - Prob. 59ECh. 13.4 - Prob. 60ECh. 13.4 - Prob. 61ECh. 13.4 - Prob. 62ECh. 13.4 - Prob. 63ECh. 13.4 - On the basis of material in this section, or your...Ch. 13.5 - Refer to the stock table (Table 14 on page 749)...Ch. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Finding Stock Costs Find the basic cost (ignoring...Ch. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Finding Stock Costs Find the cost, at the day's...Ch. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Finding Stock Costs Find the cost, at the day's...Ch. 13.5 - Prob. 22ECh. 13.5 - Prob. 23ECh. 13.5 - Finding Stock Costs Find the cost, at the day's...Ch. 13.5 - Prob. 25ECh. 13.5 - Prob. 26ECh. 13.5 - Finding Receipts for Stock Sales Find the amount...Ch. 13.5 - Prob. 28ECh. 13.5 - Prob. 29ECh. 13.5 - Finding Receipts for Stock Sales Find the amount...Ch. 13.5 - Finding Receipts for Stock Sales Find the amount...Ch. 13.5 - Prob. 32ECh. 13.5 - Finding Net Results of Combined Transactions For...Ch. 13.5 - Finding Net Results of Combined Transactions For...Ch. 13.5 - Prob. 35ECh. 13.5 - Costs and Returns of Stock Investments For each of...Ch. 13.5 - Prob. 37ECh. 13.5 - Prob. 38ECh. 13.5 - Total Return on Bond Investments Find the total...Ch. 13.5 - Prob. 40ECh. 13.5 - Prob. 41ECh. 13.5 - Total Return on Bond Investments Find the total...Ch. 13.5 - Net Asset Value of a Mutual Fund For each...Ch. 13.5 - Prob. 44ECh. 13.5 - Net Asset Value of a Mutual Fund For each...Ch. 13.5 - Prob. 46ECh. 13.5 - Prob. 47ECh. 13.5 - Finding Monthly and Annual Investment Returns For...Ch. 13.5 - Prob. 49ECh. 13.5 - Prob. 50ECh. 13.5 - Effective Annual Rate of Return of Mutual Fund...Ch. 13.5 - Prob. 52ECh. 13.5 - Prob. 53ECh. 13.5 - Effective Annual Rate of Return of Mutual Fund...Ch. 13.5 - Prob. 55ECh. 13.5 - Prob. 56ECh. 13.5 - Inflation-Adjusted Retirement Accounts Find the...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - The Effect of Tax Deferral on Retirement Accounts...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13.5 - Prob. 65ECh. 13.5 - Prob. 66ECh. 13.5 - Prob. 67ECh. 13.5 - Solve each problem. Comparing Continuous with...Ch. 13.5 - Prob. 69ECh. 13.5 - Prob. 70ECh. 13.5 - Spreading Mutual Fund Investments among Asset...Ch. 13.5 - Prob. 72ECh. 13.5 - Prob. 73ECh. 13.5 - Prob. 74ECh. 13.5 - Prob. 75ECh. 13.5 - Prob. 76ECh. 13.5 - Prob. 77ECh. 13.5 - Prob. 78ECh. 13.5 - Prob. 79ECh. 13.5 - Write responses to Exercises 77-84. Some research...Ch. 13.5 - Prob. 81ECh. 13.5 - Prob. 82ECh. 13.5 - Write responses to Exercises 77-84. Some research...Ch. 13.5 - Prob. 84ECh. 13 - Find all monetary answers to the nearest cent. Use...Ch. 13 - Find all monetary answers to the nearest cent. Use...Ch. 13 - Solve each problem.
3. Effective Annual Yield of...Ch. 13 - Solve each problem. Years to Double by the Rule of...Ch. 13 - Solve each problem. Finding the Present Value of a...Ch. 13 - solve each prooiem.
6. Finding Bank Card Interest...Ch. 13 - Analyzing a Consumer Loan Julio buys a koi fish...Ch. 13 - Analyzing a Consumer Loan Julio buys a koi fish...Ch. 13 - Analyzing a Consumer LoanJulio buys a koi fish...Ch. 13 - Analyzing a Consumer Loan Julio buys a koi fish...Ch. 13 - Prob. 11TCh. 13 - 12. Explain what a mutual fund is, and discuss...Ch. 13 - Prob. 13TCh. 13 - Finding the Monthly Payment on a Home Mortgage...Ch. 13 - Solve each problem. Cost of Points in a Home Loan...Ch. 13 - Prob. 16TCh. 13 - Prob. 17TCh. 13 - Prob. 18TCh. 13 - Prob. 19TCh. 13 - Prob. 20TCh. 13 - Prob. 21TCh. 13 - Prob. 22T
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- Please solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward
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Author:Swokowski
Publisher:Cengage
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY