Question

An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 4​%, on A bonds 5​%, and on B bonds 8​%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following​ conditions?

A The total investment is ​$9,000​, and the investor wants an annual return of ​$470 on the three investments.

B The values in part A are changed to ​$24,000 and ​$1,250​, respectively.

.

Answer 1

a) let amount invested in AAA = x

in A = y

in B = z

setting up the equations

x + y + z = 9000

.04x + .05y + .08z = 470

x = 2z

so, amount invested in AAA = $ 4000

in A bonds = $ 3000

in B bonds = $ 2000

b)  setting up the equations again

x + y + z = 24000

.04x + .05y + .08z = 1250

x = 2z

amount invested in AAA bonds = $ 10000

in A bonds = $ 9000

in B bonds = $ 5000