Jolene has $28000 to invest. After consulting a financial planner, she decided that the money should be invested in Treasury bills that yield 3% interest, Treasury bonds that yield 8% interest, and Corporate bonds that yield 13% interest. Jolene wants to have an annual income of $2440 from the portfolio. Find the amount in each investment type. Set up a system of equations, and then solve using your calculator. a) For this situation, there is no possible solution to this problem. an infinite number of possible solutions. exactly one realistic solution. b) Write the solutions here, using tt as the parameter as needed. Solution: x= _________invested in Treasury bills ; y= _________ invested in Treasury bonds ; and z= _________ invested in Corporate bonds. c) To meet the conditions that were outlined above, what is the minimum amount that can be invested in Coprorate bonds so that you end up with realistic non-negative answers for all investment amounts. {Hint: Play with the equations like we do in class.} must be invested in Corporate bonds. How much would be invested in the other two types in this particular case? __________ invested in Treasury bills ; and ____________ invested in Treasury bonds. d) Of the many possible solutions to this problem, how much should be invested in each type of account that maximizes the amount of money invested in Corporate bonds? ___________ invested in Treasury bills, __________ invested in Treasury bonds, and _________ invested in Corporate bonds.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Jolene has $28000 to invest. After consulting a financial planner, she decided that the money should be invested in Treasury bills that yield 3% interest, Treasury bonds that yield 8% interest, and Corporate bonds that yield 13% interest. Jolene wants to have an annual income of $2440 from the portfolio. Find the amount in each investment type. Set up a system of equations, and then solve using your calculator.
a) For this situation, there is
- no possible solution to this problem.
- an infinite number of possible solutions.
- exactly one realistic solution.
x= _________invested in Treasury bills ;
y= _________ invested in Treasury bonds ; and
z= _________ invested in Corporate bonds.
c) To meet the conditions that were outlined above, what is the minimum amount that can be invested in Coprorate bonds so that you end up with realistic non-negative answers for all investment amounts. {Hint: Play with the equations like we do in class.} must be invested in Corporate bonds.
How much would be invested in the other two types in this particular case?
__________ invested in Treasury bills ; and
____________ invested in Treasury bonds.
d) Of the many possible solutions to this problem, how much should be invested in each type of account that maximizes the amount of money invested in Corporate bonds?
___________ invested in Treasury bills, __________ invested in Treasury bonds,
and _________ invested in Corporate bonds.
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