
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
Over the course of three years, Marina did not invest the funds in her Individual Investment Account (IIA) into financial instruments and therefore did not receive any income from it. However, she gained the right to an investment tax deduction for depositing her own money into the IIA.

The tax deduction is provided for the amount of money deposited into the IIA during the tax period, but not more than 400,000 rubles in total per year.

Marina is entitled to receive 13% of the amount deposited into the IIA as a refund of the Personal Income Tax (PIT) that she paid on her income.

The PIT amount deducted from Marina's annual salary is equal to \( 30,000 \text{ rubles} \times 12 \text{ months} \times 0.13 = 46,800 \text{ rubles} \).

The tax deduction for the first year is \( 100,000 \text{ rubles} \times 0.13 = 13,000 \text{ rubles} \). This amount does not exceed the PIT deducted from Marina's annual salary.

The tax deduction for the second year is \( 400,000 \text{ rubles} \times 0.13 = 52,000 \text{ rubles} \). This amount exceeds the PIT deducted from Marina's annual salary. Therefore, the tax deduction will be limited to the PIT paid for the second year, or 46,800 rubles.

The tax deduction for the third year is \( 400,000 \text{ rubles} \times 0.13 = 52,000 \text{ rubles} \). This amount also exceeds the PIT deducted from Marina's annual salary. Therefore, the tax deduction will be limited to the PIT paid for the third year, or 46,800 rubles.

The total amount of tax deduction for 3 years is \( 13,000 + 46,800 + 46,800 = 106,600 \text{ rubles} \).

The return on Marina's transactions over 3 years is \( \frac{106,600}{1,000,000} \times 100 \% = 10.66 \% \).

The annual return on Marina's transactions is \( \frac{10.66 \%}{3} = 3.55 \% \).

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