Question 1072152: A $70,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $6430 annual income from the investments, how much should the bank invest in bonds?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A $70,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%.
The bond and CD investment together must equal the mortgage investment.
To earn a $6430 annual income from the investments, how much should the bank invest in bonds?
:
let b = amt invested in bonds
let c = amt invested in CD's
let m = amt invested in Mortgages
:
b + c + m = 70000
:
"The bond and CD investment together must equal the mortgage investment."
m = (b+c)
therefore we can replace m with (b+c)
b + c + (b+c) = 70000
2b + 2c = 70000
simplify, divide by 2
b + c = 35000
c = 35000 - b; we can use this form for substitution
:
"To earn a $6430 annual income from the investments, how much should the bank invest in bonds?"
.09b + .07c + .10m = 6430
Replace m with (b+c)
.09b + .07c + .10(b+c) = 6430
.09b + .07c + .10b + .10c = 6430
.19b + .17c = 6430
Replace c with (35000-b)
.19b + .17(35000-b) = 6430
.19b + 5950 - .17b = 6430
.19b - .17b = 6430 - 5950
.02b = 480
b = 480/.02
b = $24,000 in vested in bonds
:
:
:
Confirm this by finding c and m, then finding the total interest
c: 35000-24000 = 11000
m: 24000+11000 = 35000
.09(24000) = 2160
.07(11000) = 770
.10(35000) = 3500
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total int: 6430
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