SOLUTION: A person has 30,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury Bills yielding 2%, Treasury Bonds yielding 4% and Corporat
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Question 1106454: A person has 30,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury Bills yielding 2%, Treasury Bonds yielding 4% and Corporate Bonds yielding 6%. The person wants an annual income of $1120 and the amount invested in Corporate Bonds must be half that in Treasury Bills. Find amount for each. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A person has 30,000 to invest.
a + b + c = 30000
As the person's financial consultant, you recommend that the money be invested in:
Treasury Bills yielding 2%,
let a = T bills
Treasury Bonds yielding 4% and
let b = T bonds
Corporate Bonds yielding 6%.
let c = Corp bonds
The person wants an annual income of $1120
.02a + .04b + .06c = 1120
:
and the amount invested in Corporate Bonds must be half that in Treasury Bills.
b = a
or
a = 2b
:
replace a with 2b in both equations
2b + b + c = 3000
3b + c = 30000
and
.02(2b) + .04b + .06c = 1120
.08b + .06c = 1120
.08b = -.06c + 1120
Divide eq by .08
b = -.75c + 14000
Substitute this equation in 3b + c = 3000
3(-.75c+14000) + c = 30000
distribute the 3
-2.25c + 42000 + c = 30000
-1.25c = 30000 - 42000
-1.25c = -12000
c = -12000/-1.25
c = +$9600 in Corp bonds
Find b
b = -.75(9600) + 14000
b = -7200 + 14000
b = $6800 in T bonds
Find a
a = 2(6800)
a = $13600 in T bills
:
Find amount for each. $13600, $6800, $9600
:
:
confirm this
.02(13600) = 272
.04(6800) = 272
.06(9600) = 576
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total income: 1120
