An investor has at most $30,000 to invest in government bonds, mutual funds, and

Question

An investor has at most $30,000 to invest in government bonds, mutual funds, and money market funds. The average yeilds for the GB, MF, and MMF are 3%, 8%, and 7% respectively. The investors policy requires that the total amount invested in mutual and money market funds not exceed the amount invested in government bonds. How much should be invested in each type of investment in order to maxmize the return? What is the maximum return in the first year?

How much should be invested in government bonds? ____$

How much should be invested in mutual funds? ___$

How much should be funded in money market funds? ____$

What is the maximum return in the first year? ____$

Explanation / Answer

From the given question,

Total investment=$ 30000

let the investment in govenment bond=x

investment in mutual fund=y

investment in money market fund=z

x+y+z=30000

replacing z=30000-x-y

x>(y+z)

x>(y+30000-x-y)

2x>30000

x>15000

maximize: 0.03x+0.08y+0.07z

= 0.03x+0.08y+0.07(30000-x-y)

=2100-0.97x-0.92y

To maximize return,

Investment in govt bond=$15000

Investment in mutual fund=$15000

Investment in money market fund=$ 0

Maximum return in first year=0.03*15000+0.08*15000

=$ 1650

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