Alex needs to borrow\( \$10,\!000\) from the bank.
The bank gives him two options.
1. A ten-year loan with an annual interest rate of \(10\%\) compounded quarterly, with the condition that at the end of 5 years Alex must make a payment equal to half of his balance. At the end of the ten years, Alex will pay off the remaining balance.
2. A ten-year loan with a simple annual interest rate of \(12\%.\) With just one lump-sum payment at the end of the ten years.
Find the positive difference between the total amounts Alex has to pay back under the two schemes. Round your answer to the nearest dollar.
thx in advance