
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
Marcie needs to borrow $\$20,000$ from the bank. The bank offers her two options:

1. A fifteen-year loan with an annual interest rate of $8\%$ compounded semi-annually. At the end of 10 years, Marcie must make a payment equal to one-third of the amount she owes at that time. The remaining amount will continue to accrue interest, and Marcie will pay off the rest at the end of the fifteen years.

2. A fifteen-year loan with a simple annual interest rate of $9\%$, with a single payment due at the end of the fifteen years.

Calculate the positive difference between the total amounts Marcie would have to pay back under the two options. Round your answer to the nearest dollar.

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