SOLUTION: You have $500,000 in an IRA when you retire. You have the option of investing this money in two funds. A Plan pays 5.2% annually, B Plan pays 7.7% annually. How should you divid

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Question 178564: You have $500,000 in an IRA when you retire. You have the option of investing this money in two funds. A Plan pays 5.2% annually, B Plan pays 7.7% annually.
How should you divide your money between Plan A & Plan B to produce an annual interest income of $34,000?
This is what I have come up with so far:
Plan A + Plan B = $34,000
Plan A = 5.2%
Plan B = 7.7%
IRA =$500,000
Then I'm not sure here what to do next?

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
ok. you are just slightly off on your thinking. What your looking for is how much money is going to go into each Plan out of the $500,000. Lets call the amount invested in Plan A and Plan B, a and b respectively
:
so the total of these will be 500,000, not 34000.
:
so we have :
a+b=500000..........eq 1
:
next we do have something that does equal 34000. the interest rate of Plan A times the amount invested in plan A plus the interest rate of Plan B times the amount invested in Plan B will equal the interest income which is 34000
:
.052a+.077b=34000...eq 2
:
rewrite eq 1 to a=500000-b and plug that value into eq 2
:
.052(500000-b)+.077b=34000
:
26000-.052b+.077b=34000
:
-.25b=-8000
:
$amount invested at 5.2%
:
$amount invested at 7.7%