SOLUTION: John has $5000 to invest. Part he wishes to invest in an insured account that gives 4% annual return; however, he would like to invest in a non-insured mutual fund that gives a 7%

Question 1099292: John has $5000 to invest. Part he wishes to invest in an insured account that gives 4% annual return; however, he would like to invest in a non-insured mutual fund that gives a 7% annual return. How much should he invest in each so that the combined return is 6% annually?
Found 2 solutions by jorel1380, greenestamps:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let n and 5000-n be the amounts to be invested at 7% and 4%, respectively. Then:
.07n+.04(5000-n)=.06(5000)
.03n=100
Solve for n
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Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Here is a different method for solving this kind of problem -- described first informally, then with a formal mathematical process.

Informally...
The 6% is twice as close to 7% as it is to 4%; that means twice as much must be invested at 7% as at 4%.
So 2/3 of the $5000 must be invested at 7% and 1/3 of it at 4%.

The same process, formally...
The process is called alligation. If you haven't heard of it and are interested in learning more about it, do an internet search...

Start with a "tic-tac-toe" game board:

Put the percentages of the two accounts in the top and bottom cells of column 1, and put the combined percentage in the middle cell:

Working diagonally, put the positive difference between the numbers in column 1 and the number in column 2 in the appropriate cells in column 3:

The 2 and 1 in column 3 tell you that the money must be invested in the ratio 2:1.
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