Question

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 = $

Answer 1

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.

Answer 2

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.