
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
A client of a brokerage company deposited 10,000 rubles into a brokerage account with an exchange rate of 50 rubles per dollar, instructing the broker to invest the amount in foreign bank bonds with a guaranteed annual return of 12% in dollars.

(a) Calculate the amount in rubles that the client withdrew from their account after one year, given that the exchange rate was 80 rubles per dollar, the currency conversion commission was 5%, and the broker's commission was 30% of the profit in foreign currency.

(b) Determine the effective annual rate of return on the investment in rubles.

(c) Explain why the real annual rate of return may differ from the rate calculated in part (b). In what direction will it differ from the aforementioned rate?

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