
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
Carmen is borrowing $\$15,000$ from a bank. The bank offers her a choice between two $8$-year loan repayment plans:

${\bf Plan~1.}$ Carmen's debt accumulates $8\%$ annual interest which compounds quarterly. She pays off a third of her balance after $4$ years, and the rest at the end of the $8$ years.

${\bf Plan~2.}$ Carmen's debt accumulates $8\%$ annual interest which compounds annually. She pays off $5,000$ after $4$ years, and the rest at the end of the $8$ years.

What is the (positive) difference between Carmen's total payments under Plan 1 and Plan 2? Round to the nearest dollar.

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