Stocks, bonds, and money market

Question

Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 12%/year, while the bonds and the money market account pay 8%/year and 4%/year, respectively. The Garcias have stipulated that the amount invested in stocks should be equal to the sum of the amount invested in bonds and 3 times the amount invested in the money market account. How should the Garcias allocate their resources if they require an annual income of $10,000 from their investments? Give two specific options. (Let x1, y1, and z1 refer to one option for investing money in stocks, bonds, and the money market account respectively. Let x2, y2, and z2 refer to a second option for investing money in stocks, bonds, and the money market account respectively.)

Answer 1

invest 100K, stocks, bonds, money market returns = 12, 8 and 4%

stock investment = bond investment + 3 times money market account

need 10K income annually

give 2 options, x1, y1, z1 for stocks, bonds & money market

option 2: x2, y2, z2

x2 = y1+3z1

.12x2 + .08y1 + .04z1 = 10K

.12(y1 +3z1) + .08y1 + .04z1 = 10K

.2y1 +.4z1 = 10K

y1 +3z1 = 5K

y1 = 1K, z1 = 5J.3, x1 =5K is one option

y2 =2K, z2 = 1K, x2=5K is a 2nd option