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An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is ​%, on A bonds ​%, and on B bonds ​%. 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 if the total investment is ​$​, and the investor wants an annual return of ​$ on the three investments.

Sagot :

Answer:

The investor should invest $4,000 in AAA bonds, $3,000 in A bonds, and $2,000 in B bonds.

Explanation:

Note: This question is not complete as all the data in it are omitted. The complete question with the omitted is therefore presented before answering the question as follows:

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? How much should be invested in each type of bond if the total investment is $9,000, and the investor wants an annual return of $560 on the three investments.

The explanation of the answer is now given as follows:

From the question, we have:

AAA = 2B

Total investment is therefore as follows:

2B + A + B = $9,000

3B + A = $9,000 …………………………. (1)

Annual return is also as follows:

(5% * 2B) + (6% * A) + (9% * B) = $560

0.1B + 0.06A + 0.09B = $560

0.1B + 0.09B + 0.06A = $560

0.19B + 0.06A = $560 …………………. (2)

From equation (1), we have:

A = $9,000 – 3B …………………………. (3)

Substituting A from equation (3) into equation (2), we have:

0.19B + 0.06($9,000 – 3B) = $560

0.19B + 540 – 0.18B = $560

0.19B  – 0.18B = $560 - $540

0.01B = $20

B = $20 / 0.01

B = $2,000

Since:

AAA = 2B

Therefore, we have:

AAA = 2 * $2,000

AAA = $4,000

Substituting B = $2,000 into equation (3), we have:

A = $9,000 – (3 * $2,000)

A = $9,000 - $6,000

A = $3,000

By implication, we have total investment as follows:

AAA + A + B = $4,000 + $3,000 + $2,000 = $9,000

Therefore, the investor should invest $4,000 in AAA bonds, $3,000 in A bonds, and $2,000 in B bonds.