SOLUTION: A $132,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $1

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A $132,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $1      Log On


   

Question 1138669: A $132,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $11,200 annual income from the investments, how much should the bank invest in bonds?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount invested in CDs
Let +b+ = amount invested in bonds
Let +c+ = amount invested in mortgages
--------------------------------------------------
Use simple interest formula
+I+=+P%2Ar%2At+
(1) +a+%2B+b+%2B+c+=+132000+
(2) +I%5B1%5D+%2B+I%5B2%5D+%2B+I%5B3%5D+=+11200+
For CDs:
(3) +I%5B1%5D+=+a%2A.06%2A1+
For bonds:
(4) +I%5B2%5D+=+b%2A.08%2A1+
For mortgages:
(5) +I%5B3%5D+=+c%2A.1%2A1+
and
(6) +a+%2B+b+=+c+
--------------------------------
I can substitute (3), (4), and (5) into (2)
(2) +.06a+%2B+.08b+%2B+.1c+=+11200+
(2) +6a+%2B+8b+%2B+10c+=+1120000+
(2) +3a+%2B+4b+%2B+5c+=+560000+
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Subtracting (6) from (1)
+2c+=+132000+
+c+=+66000+
and
(2) +3a+%2B+4b+%2B+5%2A66000+=+560000+
(2) +3a+%2B+4b+=++560000+-+330000+
(2) +3a+%2B+4b+=+230000+
Multiply both sides of (1) by 2 and
subtract (1) from (2)
(1) +4a+%2B+4b+=+264000+
(2) +-3a+-+4b+=+-230000+
-------------------------------
+a+=+34000+
and
(6) +a+%2B+b+=+c+
(6) +34000+%2B+b+=+66000+
(6) +b+=+32000+
---------------------------------
$34,000 = amount invested in CDs
$32,000 = amount invested in bonds
$66,000 = amount invested in mortgages
---------------------------------------------
check:
(2) +.06a+%2B+.08b+%2B+.1c+=+11200+
(2) +.06%2A34000+%2B+.08%2A32000+%2B+.1%2A66000+=+11200+
(2) +2040+%2B+2560+%2B+6600+=+11200+
(2) +11200+=+11200+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A $132,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $11,200 annual income from the investments, how much should the bank invest in bonds?
Let amount invested in bonds, CDs, and mortgages be B, C, and M, respectively

Then we get: B + C + M = 132,000 ------ eq (i)

Also, B + C = M ------- eq (ii)

And, .08B + .06C + .1M = 11,200_____2(.04B + .03C + .05M) = 2(5,600)_____.04B + .03C + .05M = 5,600 ------- eq (iii)



2M = 132,000 ------ Substituting M for B + C in eq (i)

matrix%281%2C5%2C+M%2C+%22=%22%2C+%22132%2C000%22%2F2%2C+%22=%22%2C+%22%2466%2C000%22%29, and so, B + C = 66,000 ======> C = 66,000 - B

.04B + .03(66,000 - B) + .05(66,000) = 5,600 ------ Substituting 66,000 - B for C, and 66,000 for M in eq (iii)

.04B + 1,980 - .03B + 3,300 = 5,600

.04B - .03B = 5,600 - 5,280

.01B = 320

Amount invested in bonds, or