A person has $50,000 to invest. As the person\'s financial consultant, you recom

Question

A person has $50,000 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 $ 2970, and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.

What is the solution? Select the correct choice below and fill in any answer boxes within your choice.

A. There is one solution. The amount in treasury bills is $____, the amount in treasury bonds is $_____, and the amount in corporate bonds is $____.

(Type integers or decimals.)

B. There are infinitely many solutions. The amount in treasury bills is $_____, the amount in treasury bonds is $____, and the amount in corporate bonds is $z, where z is any real number.

(Simplify your answers.)

C. There is no solution.

Explanation / Answer

let the amount invested in Treasury bills = x

then amount invested in corporate bonds = x/2

amount invested in treasury bond = 50,000 - ( x+x/2) = 50,000 - 3x/2

treasury bills that yield 3 %, Treasury bonds that yield 6 %, and corporate bonds that yield 9 %.

equation becomes

.03x + .06( 50,000 - 3x/2 ) +.09 x/2 = 2970

.03x + 3000 - .18x / 2 + .09x/2 = 2970

.06x/2 - .18x/2 +.09x/2 = 2970 - 3000

-.03x/ 2 = -30

x = 2000

treasury bill = $ 2000

corporate bonds = $ 1000

treasury bond = 50,000 - ( 3*2000/2 ) = $ 47000

there is one solution

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