1. The following equation was estimated using the data in CEOSAL1: log(salary) = 4.322 + .276 log(sales) + .0215 roe (.324) (.033) n = 209, R² = .282. .00008 roe? (.0129) (.00026) This equation allows roe to have a diminishing effect on log(salary). Is this generality necessary? Explain why o why not.
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- You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?We are considering investing in three stocks. The randomvariable Si represents the value one year from now of $1invested in stock i. We are given that E(S1) 1.15, E(S2) 1.21, E(S3) 1.09; var S1 0.09, var S2 0.04, var S3 0.01; cov(S1, S2) 0.006, cov(S1, S3) 0.004, and cov(S2,S3) 0.005. We have $100 to invest and want to have anexpected return of at least 15% during the next year.Formulate a QPP to find the portfolio of minimum variancethat attains an expected return of at least 15%.
- The person says that 2173 is a prime number because it ends in the number3, and since 3 is a prime number then that means that 2173 is a prime number. Is2173 a prime number? What can you conclude about this person’s reasoning? Explain your answer.Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 20x + 12y + 12z subject to the following. x + z ≤ 45 x + y ≤ 30 y + z ≤ 45 (x,y,z)= f=This section contains questions regarding the 2nd part of the Unit 1 with the following topics: 1. Financial Planning2. Savings and budgeting3. Investing 1.Mutual Fund is when an investor directly acquires a claim on a security or property True False 2. The "Rule of 75" is used to determine the number of yearss needed to double the value of your money * True False
- Use the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 7x + 8y subject to x + 2y ≤ 10 x + y ≤ 7 (x,y)= f=Use the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 3x + 22y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 (x,y)= f=Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.
- We must invest all our money in two stocks: x and y.The variance of the annual return on one share of stock x isvar x, and the variance of the annual return on one share ofstock y is var y. Assume that the covariance between theannual return for one share of x and one share of y is cov(x,y). If we invest a% of our money in stock x and b% in stocky, then the variance of our return is given by a2var xb2var y2ab cov(x, y). We want to minimize the variance of thereturn on our invested money. What percentage of the moneyshould be invested in each stock?Suppose we are borrowing $1,000 at 12% annual interestwith 60 monthly payments. Assume equal payments aremade at the end of month 1, month 2, . . . month 60. Weknow that entering into Excel the functionPMT(.01, 60, 1,000)would yield the monthly payment ($22.24).It is instructive to use LP to determine the montly payment. Let p be the (unknown) monthly payment. Each monthwe owe .01 (our current unpaid balance) in interest. Theremainder of our monthly payment is used to reduce the unpaid balance. For example, suppose we paid $30 each month.At the beginning of month 1, our unpaid balance is $1,000.Of our month 1 payment, $10 goes to interest and $20 topaying off the unpaid balance. Then we would begin month2 with an unpaid balance of $980. The trick is to use LP todetermine the monthly payment that will pay off the loan atthe end of month 60.Suppose you are going to receive $20,000 per year forfive years. The appropriate interest rate is 7 percent.a. What is the present value of the payments if they are in the form of an ordinaryannuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future valueif the payments are an ordinary annuity? What if the payments are an annuitydue?c. Which has the highest present value, the ordinary annuity or annuity due? Whichhas the highest future value? Will this always be true?