4. Twin brothers, Anton Sergeyevich, a civil aviation pilot by profession, and Mikhail Sergeyevich, a neurologist, born on 05.06.1977, decided to go on vacation together and purchase a life and health insurance policy for 2,000,000 rubles. Anton Sergeyevich and Mikhail Sergeyevich had the same height - 187 cm and weight - 98 kg. Mikhail Sergeyevich decided to preliminarily calculate the cost of the policy on the insurance company's website. He looked at the rates and, without consulting and filling out the application, concluded that the cost of the insurance was the same for both brothers. Find the difference in the cost of the brothers' policies using the data in the appendix, given that insurers apply increasing coefficients for the insured person's belonging to a high-risk profession and excess weight (increased risk of cardiovascular diseases). (24 points)

Appendix: Body Mass Index (BMI) formula: BMI = weight (kg) / height^2 (m) (weight in kilograms must be divided by the square of the height, expressed in meters)

Increasing coefficients for BMI:

| BMI Range | 25-29 | 30-35 | 36-40 |
| :--- | :---: | :---: | :---: |
| Increasing Coefficient | 1 | 1.2 | 1.7 |

Increasing coefficient for occupation class:

pilot of civil aviation 1.5; neurologist 1.02

Basic rates:

|  | basic rate age \ gender |  |  |  | basic rate age \ gender |  |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Age | male | female |  | Age | male | female |
| **31** | 0.21 | 0.12 |  | **41** | 0.33 | 0.22 |
| **32** | 0.22 | 0.12 |  | **42** | 0.35 | 0.24 |
| **33** | 0.22 | 0.14 |  | **43** | 0.38 | 0.25 |
| **34** | 0.22 | 0.14 |  | **44** | 0.41 | 0.25 |
| **35** | 0.24 | 0.15 |  | **45** | 0.42 | 0.28 |
| **36** | 0.25 | 0.17 |  | **46** | 0.5 | 0.32 |
| **37** | 0.26 | 0.18 |  | **47** | 0.55 | 0.32 |
| **38** | 0.28 | 0.18 |  | **48** | 0.61 | 0.4 |
| **39** | 0.3 | 0.2 |  | **49** | 0.66 | 0.4 |
| **40** | 0.32 | 0.21 |  | **50** | 0.74 | 0.43 |
# Solution:

Let's calculate the age. Both men are 40 years old. The base rate is $0.32\%$. By occupation class: Mikhail (doctor) $0.32\% \times 1.02 = 0.3264\%$.

Anton (pilot) $0.32\% \times 1.5 = 0.48\%$.

Calculate the BMI $= 98 / 1.87^2 = 98 / 3.4969 = $ (approximately) 28.025.

Find the increasing coefficient from the table. It is 1 (i.e., there is no increasing coefficient).

Apply the final rate: $2000000 \times 0.48\% = 9600$ (Anton) and $2000000 \times 0.3264\% = 6528$.

Answer: The difference in the cost of the insurance policies is 3072 rubles.

## Grading Criteria:

1) All calculation steps are correct, and the correct answer is obtained - 24 points
2) The logic of the calculation is correct (the increasing coefficients are correctly applied), but there is an arithmetic error in the final summation or percentage calculation - up to 20 points
3) The logic of the calculation is correct (the increasing coefficients are correctly applied), but the cost of the policy was calculated without considering that the base rate is expressed as a percentage - up to 12 points
4) The BMI scale is incorrectly determined, but all other calculations are correct - up to 6 points
5) The logic of applying the rates is violated, but the increasing coefficients are correctly found - up to 3 points
6) The logic of applying the rates is violated, and the data from the appendix is incorrectly found and other issues - **0** points