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 ​$18 comma 000​, and the investor wants an annual return of ​$940 on the three investments. B.  The values in part A are changed to ​$33 comma 000 and ​$1 comma 720​, respectively. A.  The client should invest ​$ nothing in AAA​ bonds, ​$ nothing in A​ bonds, and ​$ nothing in B bonds.

Answer 1

The client invests in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 4​%, on A bonds 5​%, and on B bonds 8​% and according to the question the client wants to invest twice as much in AAA bonds as in B bonds, means
AAA = 2B

Part-A) We have,
AAA+A+B = 18000    …..(1)
0.04AAA+0.05A+0.08B = 940                       ……(2)

eq(1) can be written as : 2B+A+B = 18000
3B+A = 18000
A = 18000 - 3B           ……(3)

eq(2) can be written as : 0.04*2B+0.05A+0.08B = 940
0.08B+0.05A+0.08B = 940
0.16B+0.05A = 940
0.16B+0.05(18000 - 3B) = 940                      [by eq(3)]
0.16B+900 - 0.15B = 940
0.01B = 40
It gives B = 40*100 = $4000
Now A = 18000 – 3*4000                  [by eq (3)]
Giving A = $6000
Now AAA = 2*B = 2*4000
Giving AAA = $8000

So,
AAA = $8000
A = $6000
B = $4000

Part-B) We can repeat the same steps as in part-A by replacing the values in RHS of eq(1) and eq(2) and find the required answers.

B = $7000, AAA = $14000, A = $12000