Help please?

Question

FINANCIAL PLANNING john has $20,000 to invest.As his financial consultant ,you recommend that he invest in Treasury bills that yield 5% , Treasury bonds that yield 7% and corporate bonds that yield 9% . John wants to have an annual income of $1280 and the a,mount invested in Treasury bills must be two times the amount invested in corporate bonds.Find the amount in each investment.

Answer 1

This is a case of three linear equations with three unknowns.

The first equation is total investment. Lets say a is treasury bills, b is treasury bonds, and c is corporate bonds. Then our first equation is:

a + b + c = 20,000

Our second equation is the return. Since we get 5% on the first, 7% on the second, and 9% on the third, and we want 1280 back per year...

.05a + .07b + .09c = 1280

Finally, we have the last equation with is the amount invest in treasury bills must be twice the amount in corporate. This is the tricky equation to set-up. So if I have 10 in corporate bonds I'll have to have 20 in treasury, or a = 2c

a - 2c = 0

So now we have three equations as follows:

a + b + c = 20,000
.05a + .07b + .09c = 1280
a - 2c = 0

At this point, we want to use the equations to simplify and solve for individual variables - a matrix would be the easiest way, but then you can solve it the long way by hand - setting up the equations is the hardest part of the problem - solving them shouldn't be too hard of an excercise for you to do on your own.

Answer 2

x*0.09 +2x*0.05 +y*0.07 =1280
3x+y=20,000
y=20,000-3x so
0.19x +1400 -0.21x=1280
0.02x= 120 x = 6,000 ( inverted in corporate bonds)
y=2,000 Inverted in treasury bonds
and $12,000 inverted in treasury bills

Answer 3

The answer is 5000 and 4569. Warning: This answer might be wrong.

Answer 4

see above