
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
Jane needs to borrow $15,000 from the bank. The bank offers her two options:

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, Jane must make a payment equal to half of what she owes. The remaining half will continue to accrue interest, and at the end of fifteen years, Jane will pay off the remaining balance.

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

Calculate the positive difference between the total amounts Jane 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