4. Stanislav Petrovich, born on 05.06.1975, height 183 cm, weight 125 kg, an electrician by profession, decided to purchase life and health insurance for 5,000,000 rubles. He visited the insurance company's website, looked at the rates, and without consulting or filling out an application, concluded that the cost of the insurance was 16,000 rubles. Find the correct cost of the insurance using the data in the appendix, given that insurers apply increasing coefficients for his belonging to a high-risk profession and excessive weight (increased risk of cardiovascular diseases). (24 points)

Appendix: Body Mass Index (BMI) formula: BMI = weight (kg) / height² (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 Coef. | 1 | 1.2 | 1.7 |

Increasing coefficient for occupation class (electrician): 1.15.

Base rates:

|  | base rate age / gender |  |
| :---: | :---: | :---: |
| Age | male | female |
| **31** | 0.21 | 0.12 |
| **32** | 0.22 | 0.12 |
| **33** | 0.22 | 0.14 |
| **34** | 0.22 | 0.14 |
| **35** | 0.24 | 0.15 |
| **36** | 0.25 | 0.17 |
| **37** | 0.26 | 0.18 |
| **38** | 0.28 | 0.18 |
| **39** | 0.30 | 0.20 |
| **40** | 0.32 | 0.21 |
| **41** | 0.33 | 0.22 |
| **42** | 0.35 | 0.24 |
| **43** | 0.38 | 0.25 |
| **44** | 0.41 | 0.25 |
| **45** | 0.42 | 0.28 |
| **46** | 0.50 | 0.32 |
| **47** | 0.55 | 0.32 |
| **48** | 0.61 | 0.40 |
| **49** | 0.66 | 0.40 |
| **50** | 0.74 | 0.43 |
# Solution:

Let's calculate the age. The man is 42 years old. The base rate is $0,35 \%$. As an electrician, the rate is $0,35 \times 1,15=0,4025$.

Calculate the BMI $=125 / 1,83^{2}=125 / 3,3489=$ (approximately) $37,326$.

According to the table, we find the increasing coefficient. It is 1.7.

$0,4025 \times 1,7=0,68425-$ the final rate.

Apply it: $5000000 \times 0,68425 \%=34212,5$.

Answer: The cost of the insurance is 34212.5 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 fact that the base rate is expressed in percentages was not taken into account when calculating the policy cost - 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, the data from the appendix is incorrectly found, and other issues - **0** points