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You have 1000 euros to invest. At the beginning of each year, you can invest your available money in three different plans, Plan 1, Plan 2 and Plan 3 (available money means not blocked in a plan). Money put in Plan 1 is blocked for one year. After one year, you total interest rate is 5% (if you invested 100 euros, you will have 105 euros after one year). Money put in Plan 2 is blocked for two years. After two years, you total interest rate is 12% (if you invested 100 euros, you will have 112 euros after two years). Money put in Plan 3 is blocked for three years.Afte

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 58P: Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under...

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You have 1000 euros to invest. At the beginning of each year, you can invest your available money in three different plans, Plan 1, Plan 2 and Plan 3 (available money means not blocked in a plan).

Money put in Plan 1 is blocked for one year. After one year, you total interest rate is 5% (if you invested 100 euros, you will have 105 euros after one year).
Money put in Plan 2 is blocked for two years. After two years, you total interest rate is 12% (if you invested 100 euros, you will have 112 euros after two years).
Money put in Plan 3 is blocked for three years.After three years,you total interestrate is 19%.

Your planning horizon is 7 years. You want to maximize your available money at the end of the 7th year (again, available money means not blocked in a plan).

What would be the linear programme solving the problem.

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Hi It seems a bit empty. E.g compount intresst are not calculated in there and we should be able to invest partial amounts as well.

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Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?
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).
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?

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