Question 1155340: A person has $ 20,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills that yield 3 %, Treasury bonds that yield 6 %, and corporate bonds that yield 9 %.The person wants to have an annual income of $ 1170 comma and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A = the number of treasury bills
B = the number of treasury bonds
C = the number of corporate bonds
A + B + C = 20,000
.03A + .06B + .09C = 1170
C = 1/2 * A
solve for A to get A = 2C
replace A with 2C in both equations to get:
2C + B + C = 20,000
.03 * 2C + .06 * B + .09 * C = 1170
simplify the second equation to get:
.06 * C + .06 * B + .09 * C = 1170
combine like terms in both equations to get:
3C + B = 20,000
.15 * C + .06 * B = 1170
multiply both sides of the second equation by 20 and leave the first equation as is to get:
3C + B = 20,000
3C + 1.2B = 23.400
subtract the first equation from the second to get:
.2B = 3,400
solve for B to get:
B = 3,400 / .2 = 17,000
replace B with 17,000 in the first equation to get:
3C + B = 20,000 becomes 3C + 17,000 = 20,000
solve for C to get:
C = 1,000
since A = 2C, then A = 2,000
you have:
A = 2,000, B = 17,000, C = 1,000
A + B + C = 2,000 + 17,000 + 1,000 = 20,000
.03A + .06B + .09C = .03 * 2,000 + .06 * 17,000 + .09 * 1,000 = 60 + 1020 + 90 = 1170.
both original original equations are true when A = 2,000 and B = 17,000 and C = 1,000.
your solution is:
2,000 in treasury bills, 17,000 in treasury bonds, 1,000 in corporate bonds.
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