# Task 4. 20 points

At the beginning of 2015, Vladimir bought several kilograms of buckwheat at a price of 70 rub/kg. By the beginning of 2017, Vladimir had 1 kg of buckwheat left, and its price had risen to 85 rub/kg. It is known that at the beginning of 2015, Vladimir could open annual deposits at an interest rate of 16% per year, two-year deposits at an interest rate of 15% per year, and at the beginning of 2016, annual deposits at an interest rate of 10% per year. Interest on all deposits is paid (capitalized for two-year deposits) at the end of the year.

1) Can we conclude that Vladimir had the opportunity to allocate his funds more profitably at the beginning of 2015?
2) What monetary and non-monetary factors need to be considered to assess the optimality of Vladimir's decision?
3) If the parameters of the problem were such that in the conclusion of part (a) Vladimir could have allocated his funds more profitably at the beginning of 2015, nevertheless, we could not claim that his actions were not optimal. Why?
# Solution

(a) We know that 1 kg of buckwheat remained, which Vladimir could have bought at the beginning of 2017. Let's calculate whether it would have been profitable for him. We will consider the option where he sequentially adds money to annual deposits, and the option where he immediately puts them into a two-year deposit.

For annual deposits: he would save $70 \cdot (1+0.16) \cdot (1+0.1) = 89.32$ rubles

For a two-year deposit: he would save $70 \cdot (1+0.15) \cdot (1+0.15) = 92.57$ rubles

The exact amount saved from 70 rubles does not need to be calculated; it is sufficient to estimate that the amount of money will be more than 85 rubles.

Thus, it is clear that this amount of money would have been sufficient to buy 1 kg of buckwheat, i.e., according to the condition of the problem, Vladimir could have allocated the funds more profitably. (10 points)

(b) It is likely that part of the buckwheat could have spoiled during storage. Additionally, storing reserves for a long time requires extra space in the apartment/house, which can cause inconvenience. Having reserves can positively affect Vladimir's mood and reduce his anxiety.

Two arguments - 5 points.

(c) Our calculations are based on indicators that were unknown to Vladimir at the time of making the decision. His estimates of buckwheat prices and deposit rates in 2015 could have been such that he was acting optimally at the time, and in hindsight, it might not have been the case. (2 points)