Mortality Annuities (Excel, VBA)

Sun, 10 May 2026 15:05:00 +0100

Abstract

If you like to calculate annuities of a mortality table you have a bunch of choices:

Complex Array Formula (Worst)

Apply a complex one-cell array formula:

The names are defined as follows:

This approach has also been described at a (external link!) Google site.

Simple user defined function in VBA (Better)

A better way by far is a simple VBA function:

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Option Explicit
    
Function LiveAnnuityPV(lYears As Long, dInterestRate As Double, _
    rMortalityTable As Range) As Double
'Source (EN): https://www.sulprobil.de/mortality_annuities_en/
'Source (DE): https://www.berndplumhoff.de/mortality_annuities_de/
'(C) (P) by Bernd Plumhoff 22-Mar-2014 PB V0.1
Dim j As Long
Dim dSum As Double, dProd As Double, dPV As Double

dProd = 1#
dPV = 1#
For j = 1 To rMortalityTable.Count - lYears
    dPV = dPV / (1# + dInterestRate)
    dProd = dProd * (1# - rMortalityTable(j + lYears))
    dSum = dSum + dPV * dProd
Next j

LiveAnnuityPV = dSum

End Function

Pre-calculated Table plus an NPV Formula (Maybe Best)

The fastest and maybe best approach seems to be a pre-calculated table and an NPV formula:

Mortality Annuities on Sulprobil

Mortality Annuities (Excel, VBA)

Abstract

Complex Array Formula (Worst)

Simple user defined function in VBA (Better)

Pre-calculated Table plus an NPV Formula (Maybe Best)