# Deriving IRS Actuarial Tables H, S and R(2)

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Files Included: 2 worksheets

The course consists of two EXCEL files that demonstrate and provide the formulas behind the calculation of Actuarial Tables H, S and R(2) for valuing annuities, life estates and remainders and Actuarial Tables Z, U(1) and U(2) used in computing interests in unitrusts published by the IRS in the US. The worksheets compute:

1. For Table H, the values for the commutation functions Dx, Nx used for the calculation of the actuarial present value of a complete life annuity and Mx used in the calculation of an assurance payable at the moment of death
2. For Table S, the single life values for the annuity, life estate and remainder factors
3. For Table R(2), the remainder factors for a last-to-die joint life annuity
4. For Table Z, the values for the commutation functions Dx, Nx & Mx used for the calculation of the actuarial present value of interests in a single life unitrust
5. For Table U(1), the present valuethe remainder interest in a single life unitrust
6. For Table U(2), the present valuethe remainder interest in a unitrust due at the death of the last to die of two lives.

#### Learning Objectives

After taking this course you will be able to:

• Calculate Dx, Nx and Mx for Table H
• Calculate single life values for annuities and life estate and remainder factors for Table S
• Calculate remainder factors for last to die joint life annuity for Table R(2)
• Calculate Dx, Nx and Mx for Table Z
• Calculate the factors for the remainder interest in a single life unitrust for Table U(1)
• Calculate the factors for the remainder interest in a joint last to die unitrust for Table U(2)

#### Prerequisites

Knowledge and familiarity with life annuity products and basics mathematics, probability and EXCEL.

#### Target Audience

Those interested in understanding and recreating commutation tables used by the IRS. These may include individuals involved in negotiating annuity values for settlements who lack the necessary background in actuarial mathematics or those requiring a refresher course in the subject.

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