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CAN YOU HELP ME WITH THIS MATH WORD PROBLEM INVOLVING INVESTMENTS?
Ok this is for applied business math and this homework question is one that my professor did not teach. Any help is much appreciated.
Carletta has $10,000 to invest. As her financial consultant, you recommend that she invest in Treasury Bills that yield 6%, Treasury Bonds that yield 7%, and corporate bonds that yield 8%. Carletta wants to have an annual income of $680, and the amount invested in corporate bonds must be half that invested in Treasury Bills. Find the amount in each investment.
1 Answer
- MohammadLv 78 years agoFavorite Answer
1. Let X be Treasury Bills, Y be Treasury Bonds. Corporate Bonds will be X/2 as indicated in the question. The values of the three type of investments can be found through the following equations:
A) X + X/2 + Y = $10,000
B) (X * 6/100) + [(X/2) * 8/100] + Y *7/100 = 680 ..... By rewriting, (B) will be:
6X/100 + 4X/100 + 7Y/100 = 680
By multiplying B with 100:
C) 6X + 4X +7Y = 68,000
............. Or ..............
D) 10X + 7Y = 68,000
By multiplying (A) with 2, we get:
E) 2X + X + 2Y = 20,000 Or
F) 3X + 2Y = 20,000
Multiply (D) By 2:
G) 20X + 14 Y = 136,000
Multiply (F) by 7:
H) 21X + 14Y = 140,000
Substract (G) from (H):
I) X = 4000 ..... Treasury Bills
J) Corporate Bonds = X/2 = 4000/2 = 2000
K) Treasury Bonds = 10,000 - (4000+2000) = 4000
Proof:
---------
(4000* 6/100) + (4000 *7/100) + (2000 * 8/100) + = 680
.................... OR ...............
240 + 280 + 160 = 680.
.
.
Source(s): Arithmetic . .
