[aahuja1]

hi I'm desperately trying to answer this question:
3. A couple has $40,000 to invest. As their financial consultant, you recommend they invest some money in treasury bills that yield 6%, some money in corporate bonds that yield 8%, and some money in junk bonds that yield 10%. Prepare a table showing some of the ways this couple can achieve $3,000 per year in income.


So far I realize I have to solve for a linear equation with infinite solutions but don't have the correct answers... Here's what I've got so far:

40,000 invested between 3 different securities

Option A Investment Interest
treasury 6% 10000 600
corporate 8% 10000 800
junk 10% 20000 2000
Total Interest 3400


Option B
treasury 6% 20000 1200
corporate 8% 10000 800
junk 10% 10000 1000
Total Interest 3000



Option C
treasury 6% 20000 1200
corporate 8% 1000 80
junk 10% 19000 1900
Total Interest 3180


Option D
treasury 6% 5000 300
corporate 8% 25000 2000
junk 10% 10000 1000
Total Interest 3300

[ebaines]

I would suggest that you fix one of the variables to some value, and then see how the other two investments could be made so that the total adds to $3K. This will get you two equations in two unknowns, which you can solve. For example, fix the T-Bill amount at $20,000, which will generate $1200. That means the remaining $20K has to generate $1800. You end up with 2 equations like this:

$1800 = .08*Corp + .10*Junk
Corp + Junk = $20K

Solve, and you'll see that in this case Corp = $10K and Junk= $10.

Now try with a few different values for T-Bills, and you'll have your table.

[asterisk_man]

Maybe I'm missing how this is hard. Just pick some randomly smallish numbers for two types and calculate what the third must be to make the interest equal $3000.
Interest=0.06*T+0.08*C+0.10J

[ebaines]

Maybe I'm missing how this is hard. Just pick some randomly smallish numbers for two types and calculate what the third must be to make the interest equal $3000.
Interest=0.06*T+0.08*C+0.10J

You're missing the fact that the total investment is $40K. Hence you need the constraint that T+C+J = 40K.