Question

Question 10 (14 points) A credit union wants to make investments in the following: 10 Annual Rate Type of Investment of Retum (%) Vehicle loans 7 Consumer loans 9 Other secured loans Signature loans 11 Risk-free securities 8 The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: 1). Risk-free securities may not exceed 40% of the total investment, but must comprise at least 5% of the total. 2). Signature loans may not exceed 20% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans) 3). Consumer loans plus other secured loans may not exceed the vehicle loans 4). Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. Please set up the model to help decide how should the money be allocated to each alternative to maximize annual return? (Please use Xi to Xs for the amount of money invested in vehicle loans, consumer loans. other secured loans, signature loans, and risk-free securities).

Answer 1

After trying various permutations and combinations, the following model of allotment for each alternative to maximize annual return is arrived-

X1 - vehicle loan - 30%

X2 - consumer loan - 10%

X3 - other secured loan - 15%

X4 - signature loan - 15%

Risk free securities - 30%

By investing in this way, the total available funds of$2.5mio will fetch return of $52,500 on vehicle loan, $22,500 on consumer loan, $37,500 on other secured loan, $41,250 on signature loan and $60,000 on risk free securities, totalling $213,750.

This mode hashas made sure of all the criterias mentioned in the question are satisfied.