An algebra student has won $500,000 in a lottery and wishes to deposit it in savings accounts in two financial institutions. One account pays 11% simple interest, but deposits are insured only to $250,000. The second account pays 6.3% simple interest, and deposits are insured up to $500,000. Determine whether the money can be deposited so that it is fully insured and earns annual interest of $43,750. Can it be fully insured and earn annual interest of $43,750?
To determine whether the money can be fully insured and earn an annual interest of $43,750, we need to calculate the maximum interest that can be earned in both accounts.
Let's start with the first account, which pays 11% simple interest and is insured up to $250,000. To find the maximum interest that can be earned, we can multiply the maximum insurable amount by the interest rate:
Maximum interest in the first account = $250,000 * 11% = $27,500
Now let's move on to the second account, which pays 6.3% simple interest and is insured up to $500,000. Using the same method as above, we can calculate the maximum interest:
Maximum interest in the second account = $500,000 * 6.3% = $31,500
Next, we need to determine the total maximum interest that can be earned by adding the maximum interest from both accounts:
Total maximum interest = $27,500 + $31,500 = $59,000
Since the total maximum interest that can be earned is $59,000, which is greater than the desired annual interest of $43,750, it is possible to fully insure the money and earn an annual interest of $43,750.