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Actuarial Present Value

Fantastic work on the survival rate and expected benefit! There is one more step before us... In this lesson we will get to the most important part - actuarial present value!

Actuarial Present Value

Calculate the actuarial present value (APV) which is the sum of discounted expected benefits.

Use a recursive approach:

\( \text{APV(t)} = \text{expected_benefit(t)} + \text{APV(t+1)} \cdot v \)

where:

  • \( v = \frac{1}{1+i} \),
  • \( i \) is the monthly interest rate (interest_rate),

Remember that for the last month (maximum t), the actuarial present value equals the expected benefit.

Fill in the code:

# model.py

from settings import settings

@variable()
def actuarial_present_value(t):
    if t == settings["_____"]:
        return _____
    else:
        v = 1 / (1 + _____)
        return _____ + v * _____

Task:

  • Use the T_MAX_CALCULATION setting from settings.py,
  • Fill in the following variables: expected_benefit(t), interest_rate, actuarial_present_value(t+1).

Individual results

By default, the results are presented in the aggregated way. However, for various reasons - such as debugging - you might want to see the results for each insured person separately.

To get results for each insured person separately, set in settings.py:

# settings.py

settings = {
    "GROUP_BY": "id",
}

Task: Change the settings to get results for each insured person separately.

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