Respuesta :
Answer: bonds = $10000
CD = $39000
Mortgage = $49000
Step-by-step explanation:
Let x represent the amount that should be invested in the bond.
Let y represent the amount that should be invested in the CD.
Let z represent the amount that should be invested in the mortgage.
A $98,000 trust is to be invested in bonds paying 7%, CDs paying 5%, and mortgages paying 10%. It means that
x + y + z = 98000 - - - - - - -1
The bond and CD investment together must equal the mortgage investment. It means that
z = x + y
To earn a $7550 annual income from the investments, it means that
0.07x + 0.05y + 0.1z = 7550- - - - -- 2
Substituting z = x + y into equation 1 and equation 2, it becomes
x + y + x + y = 98000
2x + 2y = 98000
Dividing through by 2,
x + y = 49000
x = 49000 - y - - - - - - -3
0.07x + 0.05y + 0.1(x + y) = 7550
0.07x + 0.05y + 0.1x + 0.1y = 7550
0.17x + 0.15y = 7550- - - - - - - - -4
Substituting equation 3 into equation 4, it becomes
0.17(49000 - y) + 0.15y = 7550
8330 - 0.17y + 0.15y = 7550
- 0.17y + 0.15y = 7550 - 8330
- 0.02y = - 780
y = - 780/-0.02
y = 39000
x = 49000 - y = 49000 - 39000
x = 10000
Substituting x = 10000 and y = 39000 into z = x + y 1, it becomes
z = 10000 + 39000 = 49000
Answer:
The Bond Investment is $1000.
Step-by-step explanation:
Let the B denotes the Bonds Investment
CD's denoted by C
Mortgage denoted By M
and we have given that
B+C+M = 98,000 ------------------(I)
Also
B+C=M or B+C-M=0 ------------------(II)
Subtracting Eq(I) from Eq(II) we get
2M=98,000
M = 49000
Now Eq(II) Becomes
B+C = 49000
And
B= 49000-C -----------------(III)
also we have given that
Interest on Bonds = B*(7/100) = 0.07B
Interest on CD's = 0.05C
Interest on Mortgage = 0.1M
Total Interest = 0.07B + 0.05C +0.1M = 7550
(0.07)(49000-C) + (0.05)C + (0.1)(49000) =7550
3430 - 0.07C +0.05C +4900 = 7550
-0.02C + 8330 = 7550
Subtracting 8330 from both sides we get
-0.02C = - 780
Dividing -0.02 Both Sides We get
C = 39000
So substituting C =39000 in Eq(III) We get
B = 49000 -39000
B = $1000
So the Bond Investment to earn $7550 annual income from the investment is $1000.
* All Rupees are in $.
