7. Fractional Durations

  1. S. David Promislow

Published Online: 13 JAN 2011

DOI: 10.1002/9781119971528.ch7

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) Fractional Durations, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch7

Author Information

  1. York University, Toronto, Canada

Publication History

  1. Published Online: 13 JAN 2011
  2. Published Print: 17 DEC 2010

ISBN Information

Print ISBN: 9780470684115

Online ISBN: 9781119971528



  • fractional durations - cashflows at fractional durations;
  • purchasers of life annuities - purchasers of insurance policies, paying premiums monthly;
  • cashflows, discounted with interest - primed symbols denoting quantities;
  • uniform distribution of deaths - preferred method;
  • present value formulas - for fractional duration life annuities, UDD assumption for mortality;
  • immediate annuities - payments made at the end, than in the beginning;
  • due and immediate quarterly annuity payments;
  • approximation and computation - problems of obtaining numerical values;
  • fractional period premiums and reserves - unchanged, premiums paid monthly;
  • reserves at fractional durations - complete calculation of reserves on December 31


This chapter contains sections titled:

  • Introduction

  • Cashflows discounted with interest only

  • Life annuities paid mthly

  • Immediate annuities

  • Approximation and computation

  • Fractional period premiums and reserves

  • Reserves at fractional durations

  • Notes and references

  • Exercises