Problem 13. (4 points)

Nikolai, Maxim, Oxana, and Olga decided to bet on who is better at managing their money. The condition was as follows: each would invest the amount of money they could afford at the moment, but at the end of the bet, which would occur in one year, each should have a sum in rubles, obtained as a result of such investment. Nikolai invested the funds in a ruble deposit for a term of 1 year on the same day. The investment amount was 150,000 rubles. The interest rate was 7.1% per annum with monthly capitalization. Maxim bought US dollars for 80,000 rubles at the exchange rate of 58.42 rubles per 1 dollar, and placed them in a currency deposit for a term of 1 year at an interest rate of 3.6% per annum. After one year, the bank bought currency at the rate of 58.61 rubles per 1 US dollar. Oxana bought investment coins at a price of 19,704 rubles per coin for a total of 197,040 rubles. The selling price was 19,801 rubles. Olga invested 250,000 rubles in a mutual fund by purchasing shares at a price of 5,809 rubles per share. Exactly one year later, on the day the bet ended, Olga applied to the mutual fund and submitted an application to sell the shares at a price of 8,074 rubles per share. The discount on the sale of a share is 4%. Who among the friends won the bet?
# Answer: Nikolai.

## Comment:

Nikolai's return $=7.1 \%$ annually, taking into account monthly capitalization, the return at maturity will be $7.34 \%$ annually.

Maxim's return $=(80000$ rubles $/ 58.42$ rubles $) \times(1+3.6 \%) \times 58.61$ rubles $/ 80000$ rubles $\times 100 \%-100 \%=3.94 \%$

Oksana's return $=19801$ rubles $/ 19704$ rubles $\times 100 \%-100 \%=0.49 \%$.

Olga will not be able to win the bet, as by the time it ends, she will have only submitted an application to withdraw shares from the mutual fund and will not have received cash from the sale of the shares. This process requires $3-7$ days.