# You have \$12,000 to invest, and three different funds from which to choose. The municipal bond...

You have \$12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than \$2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts?

Optimal amount in municipal bonds = \$

Optimal amount in CD's = \$

Optimal in high risk amount account = \$

Optimal return expected = \$

Let the amount invested in municipal bond be x

Let the amount invested in local CD's be y

Let the amount invested in high risk account be z

Maximize, Profit = 0.07 * x + 0.08 * y + 0.12 * z

Constraints:

x + y + z = 12000 [Total amount invested must be equal to \$12,000]

z <= 2000 [Maximum amount invested in high risk account should not exceed 2000]

x >= 3*y [The amount invested in municipal funds must be atleast three times greater than local CD's]

Solving this constraints, we get

z = 2000

x = 7500 and y = 2500

Optimal amount in municipal bonds = \$7,500

Optimal amount in CD's = \$2,500

Optimal in high risk amount account = \$2,000

Optimal return expected = 0.07 * \$7500 + 0.08 * \$2500 + 0.12 * \$2000 = \$965

Note - Post any doubts/queries in comments section.

Optimal amount in municipal bonds = \$6,000

Optimal amount in CD's = \$4,000

Optimal in high risk amount account = \$2,000

Optimal return expected = 0.07 * \$6000 + 0.08 * \$4000 + 0.12 * \$2000 = \$980

Note - Post any doubts/queries in comments section.

source: Exell
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