# Task 4. Maximum 20 points

A client of a brokerage firm deposited 12,000 rubles into a brokerage account at an exchange rate of 60 rubles per dollar, instructing the broker to invest the amount in bonds of foreign banks with a guaranteed yield of $12\%$ per year in dollars.

(a) Determine the amount in rubles that the client withdrew from their account after one year, if the ruble exchange rate was 80 rubles per dollar, the currency conversion fee was $4\%$, and the broker's commission was $-25\%$ of the profit in the currency.

(b) Determine the effective (actual) annual yield on the investments in rubles.

(c) Explain why the actual annual yield may differ from the value you found in part (b). In which direction will it differ from the value found above?
# Solution and criteria for checking:

(a) The brokerage account received 12000 / $60=200$ dollars (1 point)

The stocks generated an income of $200 * 0.12=24$ dollars over the year (1 point)

At the end of the year, the account had $200+24=224$ dollars (1 point)

The broker's commission amounted to $24 * 0.25=6$ dollars (1 point)

After deducting the broker's commission, the account had $224-6=218$ dollars (1 point)

Conversion to rubles at the new exchange rate $218 * 80=17440$ rubles (1 point)

The conversion fee was $17440 * 0.04=697.6$ rubles (1 point)

The amount that can be withdrawn from the account is $17440-697.6=16742.4$ rubles (1 point)

(b) The effective return on investment in rubles was $16742.4 / 12000 * 100$ $100=39.52\%$ (points)

(c) The real annual rate of return may differ because inflation was not taken into account in the calculations. We calculated only the nominal return without considering that money could have depreciated over the year due to inflation. For example, if 12000 rubles a year ago could have bought a certain consumer basket, a nominal return of $39.52\%$ would mean that the client could now buy $39.52\%$ more of each item in the chosen consumer basket. However, the presence of inflation would not allow the number of items in the consumer basket to increase by $39.52\%$.

A detailed answer to part (c) is worth 7 points. If it is stated without explanation that the reason for the difference is inflation, only 3 points are awarded for such an answer.