
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
Thomas needs to borrow \$15,000 from a credit union. He is offered two options:

1. A twelve-year loan with an annual interest rate of \(8\%\) compounded biannually. At the end of 6 years, Thomas must make a payment equal to one-third of what he owes at that point. The remaining amount will continue to accrue interest until the end of the twelve years when Thomas will pay off the remainder.

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

Compare the total amounts Thomas has to pay back under the two schemes and determine the positive difference between these amounts. Round your answer to the nearest dollar.

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