Question

The tim, recommends that a cient invest in bonds rated AAA A, and B The average yield on AAA bonds is 5%, on A bonds 7%, and on B bonds 1296 cient 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 $29000, and the investor wants an annual return of $2,090 on the three investments B. The values in part A are changed to $33,000 and $2,300, respectively The clent should nvest sn AAA bonds, sin A bonds, and s in B bonds

Answer 1

Solution:
Given:
Yield on Bond AAA	5%
Yield on Bond A	7%
Yield on Bond B	12%
Let X be amount invested in Bond AAA
Let Y be amount invested in Bond A
Let Z be amount invested in Bond B
A)
Total investment	$29000
Annual return I.e Return on investment	$2090
Return on total Investment = (Amount invested in Bond AAA * Yield on Bond AAA)+(Amount invested in Bond A * Yield on Bond A)+
(Amount invested in Bond B * Yield on Bond B)
Return on Investment = (X * 5%)+(Y * 7%)+(Z * 12%)
$2090 = (X * 5%)+(Y * 7%)+(Z * 12%)
Total Investment = Investment in Bond AAA + Investment in Bond A + Investment in Bond B
$29000 = X+Y+Z
Given that ratio between AAA and Bond B
Amount invested in Bond AAA = 2* Amount invested in Bond B
X = 2*Z
Replacing X with 2Z in the first two equation:
First Equation:
$2090 = (X * 5%)+(Y * 7%)+(Z * 12%)
$2090 = (2Z * 5%)+(Y * 7%)+(Z * 12%)
$2090 = (0.10Z)+(0.07Y)+(0.12Z)
$2090 = 0.22Z+0.07Y
Second Equation:
$29000 = X+Y+Z
$29000 = 2Z+Y+Z
$29000 = 3Z+Y
$29000-3Z = Y
Using $29000-3Z = Y in first equation:
$2090 = 0.22Z+0.07($29000-3Z)
$2090 = 0.22Z+2030-21Z)
$2090-$2030 = 0.22Z-0.21Z
$60 = 0.01Z
Z = $60/0.01
Z= $6000
X= 2Z
X = 2*6000
X = $12000
Total investment = X + Y+ Z
$29000 = $12000+ Y+ $6000
$29000-$12000-$6000 = Y
$11000 = Y
Amount invested in Bond AAA I.e X = $12000
Amount invested in Bond A I.e Y = $11000
Amount invested in Bond B I.e Z = $6000
B)
Total investment	$33000
Annual return I.e Return on investment	$2390
Return on total Investment = (Amount invested in Bond AAA * Yield on Bond AAA)+(Amount invested in Bond A * Yield on Bond A)+
(Amount invested in Bond B * Yield on Bond B)
Return on Investment = (X * 5%)+(Y * 7%)+(Z * 12%)
$2390 = (X * 5%)+(Y * 7%)+(Z * 12%)
Total Investment = Investment in Bond AAA + Investment in Bond A + Investment in Bond B
$33000 = X+Y+Z
Given that ratio between AAA and Bond B
Amount invested in Bond AAA = 2* Amount invested in Bond B
X = 2*Z
Replacing X with 2Z in the first two equation:
First Equation:
$2390 = (X * 5%)+(Y * 7%)+(Z * 12%)
$2390 = (2Z * 5%)+(Y * 7%)+(Z * 12%)
$2390 = (0.10Z)+(0.07Y)+(0.12Z)
$2390 = 0.22Z+0.07Y
Second Equation:
$33000 = X+Y+Z
$33000 = 2Z+Y+Z
$33000 = 3Z+Y
$33000-3Z = Y
Using $33000-3Z = Y in first equation:
$2390 = 0.22Z+0.07($33000-3Z)
$2390 = 0.22Z+2310-21Z)
$2390-$2310 = 0.22Z-0.21Z
$80 = 0.01Z
Z = $80/0.01
Z= $8000
X= 2Z
X = 2*8000
X = $16000
Total investment = X + Y+ Z
$33000 = $16000+ Y+ $8000
$33000-$16000-$8000 = Y
$9000 = Y
Amount invested in Bond AAA I.e X = $16000
Amount invested in Bond A I.e Y = $9000
Amount invested in Bond B I.e Z = $8000