An investment firm recommends that a client invest in bonds rated AAA, A, and B.

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 $25,000 and the investor wants an annual return of $1,310 on the three investments.

B.The values in part A are changed to $34,000 and $1,780, respectively.

The client should invest $___ in AAA bonds, $___ in A bonds, and $___ in B bonds.

Explanation / Answer

A)

Let amount invested in A bonds =x

and amount invest in B bonds =y

it is given that client wants to invest twice as much in AAA bonds as in B bonds

so amount invested in AAA bonds =2y

x+y+2y =25000

x+3y =25000

x=25000-3y

Also

0.04*(2y) +0.05(x)+0.08(y) =1310

0.08y +0.05x +0.08y =1310

0.16y +0.05x =1310

0.16y+0.05(25000-3y)=1310

0.16y +1250-0.15y=1310

0.01y=1310-1250

y=6000

So amount invested in B =y=6000

Amount invested in AAA =2y =2(6000) =12000

Amount invested in A =x=25000-3y =25000-3(6000) =25000-18000 =7000

B)

Let amount invested in A bonds =x

and amount invest in B bonds =y

it is given that client wants to invest twice as much in AAA bonds as in B bonds

so amount invested in AAA bonds =2y

x+y+2y =34000

x+3y =34000

x=34000-3y

Also

0.04*(2y) +0.05(x)+0.08(y) =1780

0.08y +0.05x +0.08y =1780

0.16y +0.05x =1780

0.16y+0.05(34000-3y)=1780

0.16y +1700-0.15y=1780

0.01y=1780-1700

y=8000

So amount invested in B =y=8000

Amount invested in AAA =2y =2(8000) =16000

Amount invested in A =x=34000-3y =34000-3(8000) =34000-24000 =10000

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