Question 1082675: A $128,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $11,980 annual income from the investments, how much should the bank invest in bonds?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! total investment is 128,000.
it is invested in bonds paying 9%, CEDs paying 8% and mortgages paying 10%.
the sum of the bond and CD investments must equal mortgage investment.
let b equal the amount invested in bonds.
let c equal the amount invested in CDs.
let d equal the amount invested in mortgages.
total investment is 128,000
b + c + d = 128,000
total income per year is equal to 11,980.
.09b + .08c + .10d = 11,980
you have 2 equations that need to be solved simultaneously.
they are:
b + c + d = 128,000
.09b + .08c + .10d = 11,980
you are given that the sum of the bond and CD investment must be equal to the mortgage investment.
b + c = d
in the 2 equations that need to be solved simultaneously, replace d with b + d to get:
b + c + b + c = 128,000
.09b + .08c + .10(b + c) = 11,980
simplify to get:
b + c + b + c = 128,000
.09b + .08c + .10b + .10c = 11,980
combine like terms to get:
2b + 2c = 128,000
.19b + .18c = 11,980
you have now reduced the number of variables to 2 in 2 equations which can be solved.
this can be solved in various ways.
we'll use elimination.
multiply both sides of second equation by (2/.19) and leave the first equation as is to get:
2b + 2c = 128,000
2b + 1.894736842c = 126,105.2632
subtract the second equation from the first to get:
.1052631579c = 1894.736842
solve for c to get c = 1894.736841 / .1052631579 = 18,000
2c is therefore equal to 36,000
in the equation of 2b + 2c = 128,000, replace 2c with 36,000 to get:
2b + 36,000 = 128,000
solve for b to get:
b = (128,000 - 36,000) / 2.
this makes b = 46,000.
in the equation of b + c + d = 128,000, solve for d to get:
d = 128,000 - 18,000 - 46,000.
this makes d = 64,000
you have:
b = 46,000
c = 18,000
d = 64,000
b + c + d is now equal to 46,000 + 18,000 + 64,000 = 128,000
.09b + .08c + .10d is now equal to .09*46,000 + .08*18,000 + .10*64,000.
this becomes equal to 4140 + 1440 + 6400 which is equal to 11,980.
the amount invested in bonds and cd's is 18,000 + 46,000 = 64,000 which is equal to the amount invested in mortgages.
all the requirements of the problem are satisfied, so the solution looks good.
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