
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Alex needs to borrow $15,000 from the bank. The bank offers him two choices:

1. A fifteen-year loan with an annual interest rate of 8% compounded semi-annually, with a condition that at the end of 7.5 years, Alex must make a payment equal to half of what he owes. The remaining balance continues to accrue interest, and at the end of the fifteen years, Alex will pay off the remaining balance.

2. A fifteen-year loan with a simple annual interest rate of 10%, with a single lump-sum payment at the end of the fifteen 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.

Present the answer in LaTex format: \boxed{Your answer}
user