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Annuity Present Value (Actuarial)

Compute actuarial present value for whole life, temporary, and deferred life annuities.

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What This Calculator Does

Compute actuarial present value for whole life, temporary, and deferred life annuities.

It combines Age, Annuity Type, Interest Rate, Term (Years, temporary only) to estimate Actuarial Present Value (a), Actuarial Present Value (ä), Payment Frequency.

Formula & Method

Core equations: The actuarial present value of a life annuity-immediate is a_x = \sum_{k=1}^{\infty} v^k\,{}_kp_x. For temporary annuities, the sum is truncated at n. For annuity-due, payments shift one period earlier: \ddot{a}_x = \sum_{k=0}^{\infty} v^k\,{}_kp_x.

Notation used in the formulas: R = Actuarial Present Value (a); x_{1} = Age; x_{2} = Annuity Type; x_{3} = Interest Rate; x_{4} = Term (Years, temporary only); x_{5} = Deferral (Years, deferred only); x_{6} = Payment Frequency.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

  • Age: Used directly in the calculation.
  • Annuity Type: Used directly in the calculation.
  • Interest Rate: Used directly in the calculation.
  • Term (Years, temporary only): Used directly in the calculation.
  • Deferral (Years, deferred only): Used directly in the calculation.
  • Payment Frequency: Used directly in the calculation.
  • Sex: Used directly in the calculation.
  • Mortality Table: Used directly in the calculation.

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