Respuesta :
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.
