an investor has rs 30000 that he wants to invest in bank deposits, equity shares and unit trust. in view of the risk involved in buying equity shares he wants to invest an amount in equity share is equals to 20% of his total investment in bank deposits and unit trust. Because of certain tax exemptions available to him , he would like to maintain the ratio of 3:2 between investment in bank deposits and unit trust. determine the amount he would invest in each of the three forms of investment
Answers
Answer:
It is given that Rs.30,000 must be invested into two types of bonds with 5% and 7% interest rates.
Let Rs.x be invested in bonds of the first type.
Thus, Rs.(30000−x) will be invested in the other type.
Hence, the amount invested in each type of the bonds can be represented in matrix form with each column corresponding to a different type of bond as :
X=[
x
30000−x
]
A) Annual interest obtained is Rs.1800.
We know, Interest=
100
PTR
Here, the time is one year and thus T=1
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[1800]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[1800]
⇒
100
5x
+
100
7(30000−x)
=1800
⇒ 5x+210000−7x=180000
⇒ −2x=−30000
∴ x=15000
Amount invested in the first bond =x=Rs.15000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−15000)=Rs.15000
∴ The trust has to invest Rs.15000 each in both the bonds in order to obtain an annual interest of Rs.1800
B) Annual interest obtained is Rs.2000.
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[2000]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[2000]
⇒
100
5x
+
100
7(30000−x)
=2000
⇒ 5x+210000−7x=200000
⇒ −2x=−10000
∴ x=5000
Amount invested in the first bond =x=Rs.5000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−5000)=Rs.25000
∴ The trust has to invest Rs.5000 in the first bond and Rs.25000 in the second bond in order to obtain an annual interest of Rs.2000
Step-by-step explanation:
please mark as brainlist
Answer:
It is given that Rs.30,000 must be invested into two types of bonds with 5% and 7% interest rates.
Let Rs.x be invested in bonds of the first type.
Thus, Rs.(30000−x) will be invested in the other type.
Hence, the amount invested in each type of the bonds can be represented in matrix form with each column corresponding to a different type of bond as :
X=[
x
30000−x
]
A) Annual interest obtained is Rs.1800.
We know, Interest=
100
PTR
Here, the time is one year and thus T=1
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[1800]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[1800]
⇒
100
5x
+
100
7(30000−x)
=1800
⇒ 5x+210000−7x=180000
⇒ −2x=−30000
∴ x=15000
Amount invested in the first bond =x=Rs.15000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−15000)=Rs.15000
∴ The trust has to invest Rs.15000 each in both the bonds in order to obtain an annual interest of Rs.1800
B) Annual interest obtained is Rs.2000.
Hence, the interest obtained after one year can be expressed in matrix representation as -
[
x
30000−x
]
⎣
⎢
⎢
⎡
100
5
100
7
⎦
⎥
⎥
⎤
=[2000]
⇒ [x×
100
5
+(30000−x)×
100
7
]=[2000]
⇒
100
5x
+
100
7(30000−x)
=2000
⇒ 5x+210000−7x=200000
⇒ −2x=−10000
∴ x=5000
Amount invested in the first bond =x=Rs.5000
⇒ Amount invested second bond =Rx(30000−x)=Rs.(30000−5000)=Rs.25000
∴ The trust has to invest Rs.5000 in the first bond and Rs.25000 in the second bond in order to obtain an annual interest of Rs.2000
Step-by-step explanation:
Hii!! GOOD EVENING!!