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 | |||||
The tim, recommends that a cient invest in bonds rated AAA A, and B The average...
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