The employee credit union at State University is planning the allocation of fund
ID: 3175081 • Letter: T
Question
The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:
10
The credit union will have $1.9 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:
• Risk-free securities may not exceed 35% of the total funds available for investment.
• Signature loans may not exceed 12% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $1.9 million be allocated to each of the loan/investment alternatives to maximize total annual return?
What is the projected total annual return?
Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 9 Other secured loans10
Signature loans 11 Risk-free securities 9Explanation / Answer
Given,
Type of Loan/Investment
Annual Rate of Return (%)
Automobile loans
8
Furniture loans
9
Other secured loans
10
Signature loans
11
Risk-free securities
9
total fund available is 1.9 billion
let,
x1 = automobile loans
x2 = furniture loans
x3 = other secured loans
x4 = signature loans
x5 = Risk free securities
the problem can be solved using linear programming
the conditions for linear programming are given as,
solving these conditions using excel we get
x1 = automobile loans=630000
x2 = furniture loans=170000
x3 = other secured loans=460000
x4 = signature loans=140000
x5 = Risk free securities=600000
and maximum annual return is 188000 (9.5%)
Type of Loan/Investment
Annual Rate of Return (%)
Automobile loans
8
Furniture loans
9
Other secured loans
10
Signature loans
11
Risk-free securities
9
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