an algebra student won $115,000 in a lottery and wishing to deposit it in savings accounts in two financial institutions. One account pays 7.9% simple interest but only insures $60,000. The second account pays 6.9% simple interest and deposits are insured up to $100,000. Determine the maximum amount of annual interest the student can earn while keeping all money insured.

Put the maximum insured amount (60,000) in the bank paying the higher interest, and the remainder in the other bank.

7.9% x 60,000 + 6.9% x 55,000 = $8535.

All money and earnings will be insured.

To determine the maximum amount of annual interest the student can earn while keeping all the money insured, we need to find the optimal allocation of funds between the two accounts.

Let's start by determining the maximum amount that can be deposited in each account while still remaining within the insurance limits.

1. Account 1 pays 7.9% simple interest and insures up to $60,000. So, the maximum amount that can be deposited in this account is $60,000.

2. Account 2 pays 6.9% simple interest and insures up to $100,000. Since the total amount won in the lottery is $115,000, and the maximum insurable amount is $100,000, this means that $15,000 must be deposited in Account 1 to stay within the insurance limit. Therefore, the maximum amount that can be deposited in Account 2 is $100,000 - $15,000 = $85,000.

Now, we can calculate the maximum amount of annual interest the student can earn.

1. The amount deposited in Account 1 is $60,000, and it pays simple interest of 7.9%. So, the annual interest earned in this account is $60,000 * 7.9% = $4,740.

2. The amount deposited in Account 2 is $85,000, and it pays simple interest of 6.9%. So, the annual interest earned in this account is $85,000 * 6.9% = $5,865.

To find the maximum amount of annual interest, we add the interest earned from each account:

$4,740 + $5,865 = $10,605

Therefore, the maximum amount of annual interest the student can earn while keeping all the money insured is $10,605.