Question

An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 5%, on A bonds 6​%, and on B bonds 9%. 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 ​$26,000 and the investor wants an annual return of ​$1,620 on the three investments. B.  The values in part A are changed to ​$43,000 and ​$2,680​, respectively. The client should invest $___ in AAA bonds, $___ in A bonds, and $___ in B bonds.

Answer 1

ANSWER:

An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 5%, on A bonds 6​%, and on B bonds 9%. 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 ​$26,000 and the investor wants an annual return of ​$1,620 on the three investments. B. The values in part A are changed to ​$43,000 and ​$2,680​, respectively. The client should invest $___ in AAA bonds, $___ in A bonds, and $___ in B bonds.

(A)let investment in B is x ; therefore investment in AAA =2x

hence investment in A bond =26000-3x

therefore total return =x*0.09+2x*0.05+(26000-3x)*0.06 =1620

0.01x =1620-1560

x =6000

hence investment in B bond =6000

investment in AAA bond =2*6000=12000

and investment in A bond =26000-3*6000 =8000

(B)

let investment in B is x ; therefore investment in AAA =2x

hence investment in A bond =43000-3x

therefore total return =x*0.09+2x*0.05+(43000-3x)*0.06 =2680

0.01x =2680-2580

x =10000

hence investment in B bond =10000

investment in AAA bond =2*10000=20000

and investment in A bond =43000-3*10000 =13000