QUESTION: How are late retirements computed when calculations are performed annually using factors from NRD?

ANSWER: ProAdmin uses the basis at the calculation date, and late retirement factors as ratios of an immediate annuity at Normal Retirement Date to a deferred annuity from Normal Retirement Date to the calculation date.

The chart below shows example output of a Late Retirement Benefit Formula Component, where the calculations are performed annually using factors from NRD.  Line numbers are included on the left for easy reference. For this example, the mortality is SOA UP-1984 Mortality, the interest rate is 5%, the accrued benefit is $1,000 and the member’s Normal Retirement Age is 64 years 8 months which occurs during September 2023.  We want to compute the values in the column Annuity Deferred from NRD.

Benefit Formula Components
Type: Late Retirement - Calculation performed annually from NRD
Line Number	Date	Member Calc. Age	Accrued Benefit	Interest Rate	Immediate Annuity at NRD	Annuity Deferred from NRD	Incremental Late Ret. Factor (from boy)	Benefit Component
1	12/31/2021	62y 11m	1000	0.05	10.134760		1	10000
2	12/31/2022	63y 11m	1000	0.05	10.134760		1	1000
3	09/30/2023	64y 8m	1000	0.05	10.134760	10.134760	1	1000
4	12/31/2023	64y 11m	1000	0.05	10.134760	9.892455	1.024494	1024.49
5	01/28/2024	65y 0m	1000	0.05	10.134760	9.811687	1.008232	1032.93
6	02/29/2024	65y 1m	1000	0.05	10.134760	9.732800	1.016404	1041.30
7	12/31/2024	65y 11m	1000	0.05	10.134760	8.943926	1.106053	1133.14
8	12/31/2025	66y 11m	1000	0.05	10.134760	8.058077	1.099919	1257.71
9	12/31/2026	67y 11m	1000	0.05	10.134760

You will note that this first value under Annuity deferred from NRD on line 3 has no deferral period and is the immediate annuity factor at NRA and it also occurs at every date in the column Immediate Annuity at NRD. Using ProAdmin’s Administration Factor tool, we develop immediate annuity factors for ages 64 through 68; and deferred factors from the same ages to 1, 2, 3 and 4 years:

Administration Factors
Member's	Life Annuity Factors
Age	Immediate	Deferred 1 year	Deferred 2 years	Deferred 3 years	Deferred 4 years
64	10.331551	9.362332	8.459038	7.619033	6.839746
65	10.036365	9.068039	8.167559	7.332168	6.559063
66	9.741222	8.773893	7.876485	7.045988	6.279323
67	9.447326	8.481038	7.586796	6.761287	6.001224
68	9.154382	8.189143	7.298093	6.477685	5.724490

Each of the following charts represents, by line number, the computation of each entry of the Annuity deferred from NRD for lines 3 through 8.

Line 3: Compute an immediate annuity for age 64y8m
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year.  Fractional weights:  4/12 & 8/12	Final Value
NRD	64	65	64y8m	[(1-(8/12))   64]+[(8/12)   65]
64y 8m	10.331551	10.036365	64y8m	[0.333333   10.331551] + [0.666667   10.036365]	10.134760

Line 4: Compute an annuity for age 64y8m deferred to age 64y11m
1st Compute an annuity from age 64y8m deferred to age 65
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year.  Fractional weights:  4/12 & 8/12	Value
NRD	1|64	65	4m|64y8m	[(1-(8/12))    64]+[(8/12)  65]
64y 8m	9.362332	10.036365	4m|64y8m	[0.333333  9.362332] + [0.666667  10.036365]	9.811687
2nd Compute an annuity from age 64y8m deferred to age 64y11m.  Note: we want to defer 3 out of 4 months.
Age at	Factors from Previous Calculations		Desired Factor	Interpolation Period: 4 months. Fractional weights:  1/4 & 3/4	Final Value
NRD	64y8m	4m|64y8m	3m|64y8m	[(1-(3/4))   64y8m]+[(3/4)  4m|65]
64y 8m	10.134760	9.811687	3m|64y8m	[0.25  10.134760 + [0.75  9.811687]	9.892455

Line 5: Compute an annuity from age 64y8m deferred to age 65
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year. Fractional weights:  4/12 & 8/12	Final Value
NRD	1|64	65	4m|64y8m	[(1-(8/12))   64]+[(8/12)  65]
64y 8m	9.362332	10.036365	4m|64y8m	[0.333333  9.362332] + [0.666667  10.036365]	9.811687

Line 6: Compute an annuity for age 64y8m deferred to age 65y1m
1st compute an annuity from age 64y8m deferred to age 65
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year.  Fractional weights:  4/12 & 8/12	Value
NRD	1|64	65	4m|64y8m	[(1-(8/12))  1|64]+[(8/12)  65]
64y 8m	9.362332	10.036365	4m|64y8m	[0.333333  9.362332] + [0.666667  10.036365]	9.811687
2nd Compute an annuity at age 64y8m deferred to age 66
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year.  Fractional weights: 4/12 & 8/12	Value
NRD	2|64	1|65	1y4m|64y8m	[(1-(8/12))   2|64y8m]+[(8/12)  1|65]
64y 8m	8.459038	9.068039	1y4m|64y8m	[0.333333 X 8.459038] + [0.666667 X 9.068039]	8.865039
3rd Compute an annuity at age 64y8m deferred to age 66y11m. Note this is 11/12ths of the 1 year period between age 65 and age 66.
Age at	Factors from Previous Calculations		Desired Factor	Interpolation Period: 1 year. Fractional weights: 1/12 & 11/12	Final Value
NRD	4m|64y8m	1y4m|64y8m	1y3m|64y8m	[(1-(1/12))   4m|64y8m]+[(1/12)  1y4m|65]
64y 8m	9.811687	8.865039	1y3m|64y8m	[0.0833333  9.811687]+ [0.916667  8.865039]	9.732800

Line 7: Compute an annuity at 64y8m deferred to age 65y11m
Age at	Factors from Previous Calculations		Desired Factor	Interpolation Period: 1 year.  Fractional weights: 4/12 & 8/12	Final Value
NRD	4m|64y8m	1y4m|64y8m	4m|64y8m	[(1-(8/12))  4m|64y8m] + [(8/12)  1y4m|64y8m]
64y 8m	9.362332	10.036365	4m|64y8m	[0.333333  9.362332] + [0.666667  10.036365]	8.943926

Line 8: Compute an annuity at age 64y8m deferred to age 66y11m
1st Compute an annuity from age 64y8m deferred to age 66.
Age at	Factors at Integral Ages		Desired Factor	Interpolation Period: 1 year.  Fractional weights: 4/12 & 8/12	Value
NRD	2|64	1|65	1y4m|64y8m	[(1-(8/12))   2|64] + [(8/12)  1|65]
64y 8m	8.459038	9.068039	1y4m|64y8m	[0.333333  8.459038] + [0.666667  9.068039]	8.865039
2nd Compute an annuity at age 64y8m deferred to age 67
Age at	Factors at Integral Ages		Desired Factor	Interpolation   Period: 1 year.  Fractional weights:  4/12 & 8/12	Value
NRD	3|64	2|65	2y4m|64y8m	[(1-(8/12))   3|64] + [(8/12)  2|65]
64y 8m	7.619033	8.167559	2y4m|64y8m	[0.333333  7.619033] + [0.666667  8.167559]	7.984717
3rd Compute an annuity at age 64y8m deferred to age 66y11m
Age at	Factors from  Previous Calculations		Desired Factor	Interpolation Period: 1 year.  Fractional weights: 1/12 & 11/12	Final Value
NRD	1y4m|64y8m	2y4m|64y8m	1y3m|64y8m	[(1-(1/12))   1y4m|64y8m] + [(1/12)  2y4m|64y8m]
64y 8m	8.865039	7.984717	1y3m|64y8m	[0.0833333  8.865039] + [0.916667  7.984717]	8.058077

When using a single interest rate and a static mortality table, the dates to the left of Member's Calculation Age are almost irrelevant.  When using, for example, Section 417(e) assumptions the values become more complicated.  Each line of the output uses the assumptions in effect at the date to compute the Immediate Annuity at NRD and the Annuity Deferred From NRD.