SOLUTION: An algebra student has won $100.000 in a lottery and wishes to deposit it in savings account in two financial institutions. One account pays 8% simple interest, but deposits are in

Question 644469: An algebra student has won $100.000 in a lottery and wishes to deposit it in savings account in two financial institutions. One account pays 8% simple interest, but deposits are insured only to $50.000. The second account pays 6.4% simple interest, and deposits are insured up to $100.000. Determine whether the money can be deposited do that it is fully insured and earns annual interest of $7500.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
The student can't do it.
The maximum interest, while having full insurance, would to put $50,000 in first financial institution at 8%. This would yield
(1) I1 = 8/100*50000 or
(2) I1 = 4000
Then the interest from the second financial institution would be
(3) I2 = 6.4/100*50000 or
(4) I2 = 3200
Adding the interest made from each gives a maximum return of
(5) I = I1 + I2
(6) I = 7200
This is maximum because for ever dollar he/she moves from the first financial institution to the second, loses
(7) I1 - I2 = 0.08 - 0.06.4 or
(8) lose/dollar = 1.6 cents
Since the student wants full insurance coverage, he/she can only get $7,200 in interest. Not the desired $7,500. Sorry.

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