Al Ferris has $60,000 now. He wishes to invest this amount in risk free fixed income securities (Government Bonds or Fixed Deposits) in order to use the accumulation for purchasing a retirement annuity at the end of 5 years. After consulting with his financial adviser, he has been offered four types of fixed-income investments, which we will label as investments A, B, C and D.
Investments A and B are available at the beginning of each of the next 5 years (call them years 1 to 5). Each dollar invested in A at the beginning of a year returns $1.40 (a profit of $0.40) 2 years later (in time for immediate reinvestment). Each dollar invested in B at the beginning of a year returns $1.70 three years later.
Investments C and D will each be available at one time in the future. Each dollar invested in C at the beginning of year 2 returns $1.90 at the end of year 5. Each dollar invested in D at the beginning of year 5 returns $1.30 at the end of year 5.
Al wishes to know which investment plan maximizes the amount of money that can be accumulated by the beginning of year 6.
(Problem taken from “Introduction to Operations Research” by Hillier/Lieberman)
An excel solution for this problem involving 9 decision variables can be found here.