Insurance calculators

Annuity and pension value

Value of a life annuity or pension paid monthly to annually, immediate or deferred, with guaranteed periods and escalation, or the income a purchase price buys.

Inputs

Results

Cost of the income
172,851.98
Annuity factor 14.4043
Income per 100,000
6,942.36
a year
Guaranteed part
54,394.33
Life-contingent part
118,457.64

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Methodology

Conventions

  • Payments of 1/m are made m times a year, in advance or in arrears, after any deferral. Each is valued exactly on the survival curve, with no Woolhouse approximation.
  • Guaranteed payments are made for the guarantee period whether or not the annuitant is alive, once payments have begun. Escalation raises payments once a year.

References

  • Dickson, Hardy and Waters, Actuarial Mathematics for Life Contingent Risks, 3rd ed.

Formulas

Value of 1 a year
\ddot a^{(m)} = \sum_k \tfrac1m (1+e)^{\lfloor k/m \rfloor} v^{t_k}\,{}_{t_k}p_x
Income from a price
\text{income} = \text{price} / \ddot a^{(m)}