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Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Chapter 11.1, Problem 26PS
To determine
To find:
The present value with the help of given data “achieve
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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 11 Solutions
Nature of Mathematics (MindTap Course List)
Ch. 11.1 - IN YOUR OWN WORDS What is interest?Ch. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Use estimation to select the best response in...Ch. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Level 1 Use estimation to select the best response...
Ch. 11.1 - Prob. 11PSCh. 11.1 - Level 1 Use estimation to select the best response...Ch. 11.1 - Prob. 13PSCh. 11.1 - Use estimation to select the best response in...Ch. 11.1 - In Problems 15-18, calculate the amount of simple...Ch. 11.1 - Prob. 16PSCh. 11.1 - In Problems 15-18, calculate the amount of simple...Ch. 11.1 - Prob. 18PSCh. 11.1 - In problems 19-24, find the future value, using...Ch. 11.1 - Prob. 20PSCh. 11.1 - In problems 19-24, find the future value, using...Ch. 11.1 - In problems 19-24, find the future value, using...Ch. 11.1 - In problems 19-24, find the future value, using...Ch. 11.1 - In problems 19-24, find the future value, using...Ch. 11.1 - In problem 25-28, find the present value, using...Ch. 11.1 - Prob. 26PSCh. 11.1 - Prob. 27PSCh. 11.1 - In Problems2528 , find the present value, using...Ch. 11.1 - If 12,000 is invested at 4.5 for 20 years, find...Ch. 11.1 - If 34,500 is invested at 6.9 for 30 years, find...Ch. 11.1 - Find the total amount that must be repaid on the...Ch. 11.1 - Find the total amount that must be repaid on the...Ch. 11.1 - Prob. 33PSCh. 11.1 - Prob. 34PSCh. 11.1 - Compound interest Treasury notes authorized in...Ch. 11.1 - Prob. 36PSCh. 11.1 - Find the cost of each item in 5 years, assuming an...Ch. 11.1 - Find the cost of each item in 10 years, assuming...Ch. 11.1 - What is the future value after 15 years if you...Ch. 11.1 - Prob. 40PSCh. 11.1 - Suppose you see a car with an advertised price of...Ch. 11.1 - Suppose you see a car with an advertised price of...Ch. 11.1 - Suppose you buy a home and finance 285,000 at...Ch. 11.1 - Suppose you buy a home and finance 170,000 at...Ch. 11.1 - Find the cost of a home in 30 years, assuming an...Ch. 11.1 - Find the cost of the monthly rent for a...Ch. 11.1 - Suppose that an insurance agent offers you a...Ch. 11.1 - If a friend tells you she earned 5,075 interest...Ch. 11.1 - If John wants to retire with 10,000 per month, how...Ch. 11.1 - Prob. 50PSCh. 11.1 - In Problems 51-54, calculate the time necessary to...Ch. 11.1 - In problem 5154 , calculate the time necessary to...Ch. 11.1 - Prob. 53PSCh. 11.1 - Prob. 54PSCh. 11.1 - Prob. 55PSCh. 11.1 - HISTORICAL QUEST On August 8, 1981, American...Ch. 11.1 - Suppose that 1,000 is invested at 7 interest...Ch. 11.1 - Prob. 58PSCh. 11.1 - Prob. 59PSCh. 11.1 - Prob. 60PSCh. 11.2 - IN YOUR OWN WORDS What is add-on interest?Ch. 11.2 - Prob. 2PSCh. 11.2 - Prob. 3PSCh. 11.2 - IN YOUR OWN WORDS Discuss the methods of...Ch. 11.2 - Prob. 5PSCh. 11.2 - Prob. 6PSCh. 11.2 - Prob. 7PSCh. 11.2 - Use estimation to select the best response in...Ch. 11.2 - Prob. 9PSCh. 11.2 - Prob. 10PSCh. 11.2 - Prob. 11PSCh. 11.2 - Prob. 12PSCh. 11.2 - If you purchase an item for 1,295 at an interest...Ch. 11.2 - Prob. 14PSCh. 11.2 - Prob. 15PSCh. 11.2 - Prob. 16PSCh. 11.2 - Use estimation to select the best response in...Ch. 11.2 - Prob. 18PSCh. 11.2 - Prob. 19PSCh. 11.2 - Prob. 20PSCh. 11.2 - Prob. 21PSCh. 11.2 - Prob. 22PSCh. 11.2 - Prob. 23PSCh. 11.2 - Prob. 24PSCh. 11.2 - Prob. 25PSCh. 11.2 - Prob. 26PSCh. 11.2 - Prob. 27PSCh. 11.2 - Prob. 28PSCh. 11.2 - Convert each credit card rate in Problems 25-30 to...Ch. 11.2 - Convert each credit card rate in Problems 25-30 to...Ch. 11.2 - EXERCISES Calculate the monthly finance charge for...Ch. 11.2 - Prob. 32PSCh. 11.2 - EXERCISES Calculate the monthly finance charge for...Ch. 11.2 - EXERCISES Calculate the monthly finance charge for...Ch. 11.2 - EXERCISES Round your answers in Problem 3538 to...Ch. 11.2 - EXERCISES Round your answers in Problem 3538 to...Ch. 11.2 - EXERCISES Round your answers in Problem 3538 to...Ch. 11.2 - EXERCISES Round your answers in Problem 3538 to...Ch. 11.2 - EXERCISES Find the APRrounded to the nearest tenth...Ch. 11.2 - Prob. 40PSCh. 11.2 - Prob. 41PSCh. 11.2 - EXERCISES Find the APRrounded to the nearest tenth...Ch. 11.2 - EXERCISES a. Assume the cars in Problems4346can be...Ch. 11.2 - EXERCISES a. Assume the cars in Problems4346can be...Ch. 11.2 - Assume the cars in Problems 43-46 can be purchased...Ch. 11.2 - Assume the cars in Problems 43-46 can be purchased...Ch. 11.2 - A payday loan provides short-term loans ranging...Ch. 11.2 - A payday loan provides short-term loans ranging...Ch. 11.2 - Prob. 49PSCh. 11.2 - A payday loan provides short-term loans ranging...Ch. 11.2 - For each of the car loans described in Problems...Ch. 11.2 - For each of the car loans described in Problems...Ch. 11.2 - For each of the car loans described in Problems...Ch. 11.2 - For each of the car loans described in Problems...Ch. 11.2 - EXERCISES A car dealer carries out the following...Ch. 11.2 - Prob. 56PSCh. 11.2 - Prob. 57PSCh. 11.2 - Prob. 58PSCh. 11.2 - Karen and Wayne need to buy a refrigerator because...Ch. 11.2 - Rule of 78 With a typical installment loan, you...Ch. 11.3 - IN YOUR OWN WORDS What is a sequence, and what do...Ch. 11.3 - Prob. 2PSCh. 11.3 - Prob. 3PSCh. 11.3 - Prob. 4PSCh. 11.3 - Prob. 5PSCh. 11.3 - Prob. 6PSCh. 11.3 - Prob. 7PSCh. 11.3 - In Problems 5-30, a. Classify the sequences as...Ch. 11.3 - Prob. 9PSCh. 11.3 - Prob. 10PSCh. 11.3 - Prob. 11PSCh. 11.3 - Prob. 12PSCh. 11.3 - Prob. 13PSCh. 11.3 - In Problems 5-30, a. Classify the sequences as...Ch. 11.3 - Prob. 15PSCh. 11.3 - Prob. 16PSCh. 11.3 - Prob. 17PSCh. 11.3 - Prob. 18PSCh. 11.3 - In Problems 5-30, a. Classify the sequences as...Ch. 11.3 - Prob. 20PSCh. 11.3 - Prob. 21PSCh. 11.3 - Prob. 22PSCh. 11.3 - Prob. 23PSCh. 11.3 - Prob. 24PSCh. 11.3 - Prob. 25PSCh. 11.3 - Prob. 26PSCh. 11.3 - Prob. 27PSCh. 11.3 - Prob. 28PSCh. 11.3 - Prob. 29PSCh. 11.3 - In Problems 530, a. Classify the sequence as...Ch. 11.3 - Prob. 31PSCh. 11.3 - Prob. 32PSCh. 11.3 - In problems 31-46, a. Find the first three terms...Ch. 11.3 - Prob. 34PSCh. 11.3 - Prob. 35PSCh. 11.3 - Prob. 36PSCh. 11.3 - Prob. 37PSCh. 11.3 - Prob. 38PSCh. 11.3 - Prob. 39PSCh. 11.3 - Prob. 40PSCh. 11.3 - Prob. 41PSCh. 11.3 - Prob. 42PSCh. 11.3 - Prob. 43PSCh. 11.3 - Prob. 44PSCh. 11.3 - Prob. 45PSCh. 11.3 - Prob. 46PSCh. 11.3 - Prob. 47PSCh. 11.3 - Prob. 48PSCh. 11.3 - Prob. 49PSCh. 11.3 - Prob. 50PSCh. 11.3 - Prob. 51PSCh. 11.3 - Find the requested terms in Problem 4756. Find the...Ch. 11.3 - Prob. 53PSCh. 11.3 - Prob. 54PSCh. 11.3 - Prob. 55PSCh. 11.3 - Prob. 56PSCh. 11.3 - Prob. 57PSCh. 11.3 - Prob. 58PSCh. 11.3 - Prob. 59PSCh. 11.3 - Fill in the blanks so that _,8,_,_,27,_, is a. an...Ch. 11.4 - IN YOUR OWN WORDS Distinguish a sequence from a...Ch. 11.4 - Prob. 2PSCh. 11.4 - Prob. 3PSCh. 11.4 - Prob. 4PSCh. 11.4 - Find the requested value in the Problems 5-10. S5...Ch. 11.4 - Prob. 6PSCh. 11.4 - Prob. 7PSCh. 11.4 - Prob. 8PSCh. 11.4 - Prob. 9PSCh. 11.4 - Prob. 10PSCh. 11.4 - Evaluate the expression in problem 11-18. 11....Ch. 11.4 - Prob. 12PSCh. 11.4 - Prob. 13PSCh. 11.4 - Evaluate the expression in problem 11-18. 14....Ch. 11.4 - Prob. 15PSCh. 11.4 - Evaluate the expression in problem 11-18. 16....Ch. 11.4 - Prob. 17PSCh. 11.4 - Prob. 18PSCh. 11.4 - Prob. 19PSCh. 11.4 - Prob. 20PSCh. 11.4 - Prob. 21PSCh. 11.4 - Prob. 22PSCh. 11.4 - Prob. 23PSCh. 11.4 - Prob. 24PSCh. 11.4 - Prob. 25PSCh. 11.4 - Prob. 26PSCh. 11.4 - Prob. 27PSCh. 11.4 - Prob. 28PSCh. 11.4 - Prob. 29PSCh. 11.4 - Prob. 30PSCh. 11.4 - Prob. 31PSCh. 11.4 - Find the sum of the first 100 even positive...Ch. 11.4 - Prob. 33PSCh. 11.4 - Prob. 34PSCh. 11.4 - Prob. 35PSCh. 11.4 - Find the sum of the first n positive integers.Ch. 11.4 - Prob. 37PSCh. 11.4 - Find the sum of the first 50 term of the...Ch. 11.4 - Prob. 39PSCh. 11.4 - Prob. 40PSCh. 11.4 - The game of pool uses 15 balls numbered from 1to15...Ch. 11.4 - Prob. 42PSCh. 11.4 - Prob. 43PSCh. 11.4 - The game of pool uses 15 balls numbered from 1to15...Ch. 11.4 - Prob. 45PSCh. 11.4 - Prob. 46PSCh. 11.4 - How may blocks would be needed to build a stack...Ch. 11.4 - Repeat Problem 47 if the bottom row has 87 blocks.Ch. 11.4 - Prob. 49PSCh. 11.4 - The initial swing of the tip of a pendulum is 25...Ch. 11.4 - Prob. 51PSCh. 11.4 - 52. A rotating flywheel is allowed to slow to a...Ch. 11.4 - Prob. 53PSCh. 11.4 - A tennis ball is dropped from a height of 10 ft....Ch. 11.4 - A culture of bacteria increase by 100 every 24...Ch. 11.4 - Prob. 56PSCh. 11.4 - How many games are necessary for a two team...Ch. 11.4 - Prob. 58PSCh. 11.4 - Prob. 59PSCh. 11.4 - Prob. 60PSCh. 11.5 - IN YOUR OWN WORDS What do we mean by a lump-sum...Ch. 11.5 - IN YOUR OWN WORDS Why should we call an annuity a...Ch. 11.5 - Prob. 3PSCh. 11.5 - Prob. 4PSCh. 11.5 - IN YOUR OWN WORDS Distinguish an annuity problem...Ch. 11.5 - Prob. 6PSCh. 11.5 - Use a calculator to evaluate an ordinary annuity...Ch. 11.5 - Prob. 8PSCh. 11.5 - Prob. 9PSCh. 11.5 - Prob. 10PSCh. 11.5 - Use a calculator to evaluate an ordinary annuity...Ch. 11.5 - Prob. 12PSCh. 11.5 - Prob. 13PSCh. 11.5 - Prob. 14PSCh. 11.5 - Prob. 15PSCh. 11.5 - Prob. 16PSCh. 11.5 - Prob. 17PSCh. 11.5 - Prob. 18PSCh. 11.5 - Prob. 19PSCh. 11.5 - Prob. 20PSCh. 11.5 - Prob. 21PSCh. 11.5 - Prob. 22PSCh. 11.5 - In problems 2334, find the value of each of the...Ch. 11.5 - Prob. 24PSCh. 11.5 - In problems 2334, find the value of each of the...Ch. 11.5 - Prob. 26PSCh. 11.5 - In problems 2334, find the value of each of the...Ch. 11.5 - In problems 2334, find the value of each of the...Ch. 11.5 - Prob. 29PSCh. 11.5 - Prob. 30PSCh. 11.5 - Prob. 31PSCh. 11.5 - Prob. 32PSCh. 11.5 - Prob. 33PSCh. 11.5 - Prob. 34PSCh. 11.5 - Find the amount of periodic payment necessary for...Ch. 11.5 - Prob. 36PSCh. 11.5 - Find the amount of periodic payment necessary for...Ch. 11.5 - Prob. 38PSCh. 11.5 - Prob. 39PSCh. 11.5 - Find the amount of periodic payment necessary for...Ch. 11.5 - Prob. 41PSCh. 11.5 - Prob. 42PSCh. 11.5 - Prob. 43PSCh. 11.5 - Prob. 44PSCh. 11.5 - Find the amount of periodic payment necessary for...Ch. 11.5 - Prob. 46PSCh. 11.5 - Self-employed persons can make contributions for...Ch. 11.5 - The owner of Sebastopol Tree Farm deposits 650 at...Ch. 11.5 - The owner of Oak Hill Squirrel Farm deposits 1,000...Ch. 11.5 - Clearlake Optical has a 50,000 note that comes due...Ch. 11.5 - A business must raise 70,000 in 5 years. What...Ch. 11.5 - A lottery offers a 1,000,000 prize to be paid in...Ch. 11.5 - A lottery offers a 1,000,000 prize to be paid in...Ch. 11.5 - John and Rosamond want to retire in 5 years and...Ch. 11.5 - In 2012 the maximum Social Security deposit by an...Ch. 11.5 - You want to retire at age 65. You decide to make a...Ch. 11.5 - Prob. 57PSCh. 11.5 - Prob. 58PSCh. 11.5 - Clearlake Optical has developed a new lens. The...Ch. 11.5 - The owners of Bardoza Greeting Cards wish to...Ch. 11.6 - IN YOUR OWN WORDS What does amortization mean?Ch. 11.6 - Prob. 2PSCh. 11.6 - Prob. 3PSCh. 11.6 - Prob. 4PSCh. 11.6 - Use a calculator to evaluate the present value of...Ch. 11.6 - Use a calculator to evaluate the present value of...Ch. 11.6 - Prob. 7PSCh. 11.6 - Prob. 8PSCh. 11.6 - Prob. 9PSCh. 11.6 - Prob. 10PSCh. 11.6 - Use a calculator to evaluate the present value of...Ch. 11.6 - Prob. 12PSCh. 11.6 - Prob. 13PSCh. 11.6 - Prob. 14PSCh. 11.6 - Prob. 15PSCh. 11.6 - Use a calculator to evaluate the amortization...Ch. 11.6 - Prob. 17PSCh. 11.6 - Prob. 18PSCh. 11.6 - Prob. 19PSCh. 11.6 - Prob. 20PSCh. 11.6 - Prob. 21PSCh. 11.6 - Prob. 22PSCh. 11.6 - Prob. 23PSCh. 11.6 - Prob. 24PSCh. 11.6 - Prob. 25PSCh. 11.6 - Prob. 26PSCh. 11.6 - Prob. 27PSCh. 11.6 - Prob. 28PSCh. 11.6 - Prob. 29PSCh. 11.6 - Prob. 30PSCh. 11.6 - Prob. 31PSCh. 11.6 - Find the present value of the ordinary annuities...Ch. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Prob. 35PSCh. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Prob. 37PSCh. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Prob. 39PSCh. 11.6 - Prob. 40PSCh. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - Find the monthly payment for the loans in Problems...Ch. 11.6 - How much interest to the nearest dollar would be...Ch. 11.6 - How much interest to the nearest dollar would be...Ch. 11.6 - Melissa agrees to contribute 500 to the alumni...Ch. 11.6 - Arnie agrees to contribute 2,500 to the road fund...Ch. 11.6 - Prob. 49PSCh. 11.6 - Prob. 50PSCh. 11.6 - Prob. 51PSCh. 11.6 - Prob. 52PSCh. 11.6 - I recently found a real-life advertisement in the...Ch. 11.6 - Prob. 54PSCh. 11.6 - Suppose your gross monthly income is 5,500 and...Ch. 11.6 - Prob. 56PSCh. 11.6 - Prob. 57PSCh. 11.6 - Prob. 58PSCh. 11.6 - Suppose your gross monthly income is 4,550 and...Ch. 11.6 - Suppose you want to purchase a home for 425,000...Ch. 11.7 - IN YOUR OWN WORDS What are a reasonable down...Ch. 11.7 - Prob. 2PSCh. 11.7 - IN YOUR OWN WORDS Outline a procedure for...Ch. 11.7 - Prob. 4PSCh. 11.7 - Prob. 5PSCh. 11.7 - Prob. 6PSCh. 11.7 - Classify the term of financial problem for the...Ch. 11.7 - Classify the term of financial problem for the...Ch. 11.7 - Prob. 9PSCh. 11.7 - Classify the term of financial problem for the...Ch. 11.7 - Classify the type of financial formula for the...Ch. 11.7 - In Problems 12-15, match each formula in Column A...Ch. 11.7 - In Problems 12-15, match each formula in Column A...Ch. 11.7 - In Problems 12-15, match each formula in Column A...Ch. 11.7 - In Problems 12-15, match each formula in Column A...Ch. 11.7 - Classify the financial problems in Problems 16-19,...Ch. 11.7 - Classify the financial problems in Problems 16-19,...Ch. 11.7 - Classify the financial problems in Problems 16-19,...Ch. 11.7 - Classify the financial problems in Problems 16-19,...Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - Prob. 29PSCh. 11.7 - Prob. 30PSCh. 11.7 - Prob. 31PSCh. 11.7 - Prob. 32PSCh. 11.7 - Prob. 33PSCh. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - Prob. 35PSCh. 11.7 - In Problems 20-52: a. State the type; and b....Ch. 11.7 - Prob. 37PSCh. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - Prob. 41PSCh. 11.7 - Prob. 42PSCh. 11.7 - Prob. 43PSCh. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - Prob. 45PSCh. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52; a. State the type; and b....Ch. 11.7 - In Problems 20-52. a. State the type; and b....Ch. 11.7 - In Problems 20-52. a. State the type; and b....Ch. 11.7 - Problems 5355 are based on a 30-year fixed-rate...Ch. 11.7 - Problems 5355 are based on a 30-year fixed-rate...Ch. 11.7 - Problems 5355 are based on a 30-year fixed-rate...Ch. 11.7 - Problems 56-58 are based on a 30-year fixed-rate...Ch. 11.7 - Problems 56-58 are based on a 30-year fixed-rate...Ch. 11.7 - Problems 56-58 are based on a 30-year fixed-rate...Ch. 11.7 - A contest offers the winner 50,000 now or 10,000...Ch. 11.7 - In 1982 the inflation rate hit 16. Suppose that...Ch. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CR
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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
- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
- Problem 1.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%. 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.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forward
- This 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. 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(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardNote: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward
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