Glossary of Terms
Annuity A series of payments to one or more individuals,
typically over the lifetime of the recipient(s). Payments are usually made on a monthly basis but
can also be made in other frequencies such as quarterly, semi-annually, or
annually.
Annuity Due An annuity with payments made
at the beginning of the payment period, i.e., the 1st day of the
month for monthly payments. These
annuities are denoted by the double-dots (..) above the a symbol, δ.
Important Note - All
values calculated by AnnuityValue are annuity due values.
Present Value The present value of an annuity
is the single amount of dollars necessary today to pay all future payments
under the terms of the annuity. Its
important to note that the present value amount is determined by considering
both interest and mortality.
Pension plan sponsors and insurance companies typically use
these present value amounts to make benefit payments to plan participants and
beneficiaries.
Expectation of Life Based on a given mortality
table, the number of years an individual is expected to live.
Curtate Expectation of Life Based
on a given mortality table, the number of whole (complete) years
an individual is expected to live.
Joint Expectation of Life - Based on a given
mortality table, the number of years a participant and their beneficiary are both
expected to be alive.
Joint Curtate Expectation of Life - Based
on a given mortality table, the number of whole (complete) years
a participant and their beneficiary are both expected to be
alive.
Scale AA Table of rates that reflect the annual improvement
factor (as a percentage) in the mortality rate for a given age. See below for how to apply.
The Pension
Protection Act uses a phased-in method for determining the segmented interest
rates in future years.
Since
AnnuityValue is designed to handle interest rate variability for any segment
length it does NOT use the phased-in approach defined by the PPA for
determining the segmented interest rates in a given year.
For PPA
annuities, the user will have to determine the proper segmented interest rates
based on the following schedule and then select those rates in the AnnuityValue
interest rate fields.
A weighted
average of the segmented interest rates is determined as follows:
Denote
417(e)(3)(A)(ii)(II) rate as iLS
(applicable interest rate: 30
year Treasury rate for 417 lookback month)
Denote three
segmented rates as: ki1
, ki2 , ki3
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2008 |
2009 |
2010 |
2011 |
2012 |
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Years 1 5 |
.2(ki1) + .8(iLS) |
.4(ki1) + .6(iLS) |
.6(ki1) + .4(iLS) |
.8(ki1) + .2(iLS) |
ki1 |
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Years 6 20 |
.2(ki2) + .8(iLS) |
.4(ki2) + .6(iLS) |
.6(ki2) + .4(iLS) |
.8(ki2) + .2(iLS) |
ki2 |
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Years after 20 |
.2(ki3) + .8(iLS) |
.4(ki3) + .6(iLS) |
.6(ki3) + .4(iLS) |
.8(ki3) + .2(iLS) |
ki3 |
Life Annuity An annuity payable for the life
of the participant. Payments cease upon
the death of the participant.
Annuity Certain An annuity payable for a fixed
period of time, regardless of whether the participant is alive to receive it.
Annuity Certain and Continuous An
annuity which ceases on the later of (1) the death of the
participant, or (2) the passage of a fixed period of time.
Joint Annuity An annuity payable to a
participant and beneficiary as long as both the participant and
beneficiary are alive. The joint annuity
ceases to paid upon the death of either the participant or beneficiary.
Joint Annuity with Period Certain An
annuity payable to a participant and beneficiary until the later
of (1) the death of either the participant or beneficiary, or (2) the
passage of a fixed period of time.
Joint & Survivor Annuity An
annuity payable to a participant and beneficiary as long as both the
participant and beneficiary are alive, and upon the death of either
the participant or beneficiary, payments continue in an equal or reduced
amount to the survivor for the remainder of their life.
Joint & Survivor Annuity with Period Certain An
annuity payable to a participant and beneficiary in a certain amount until the later
of (1) the death of either the participant or beneficiary,
or (2) the passage of a fixed period of time, and payments continue in an equal
or reduced amount to the survivor for the remainder of their life.
Joint & Contingent Annuity An annuity
payable to a participant and beneficiary for the life of the participant,
and, upon the death of the participant, is payable in an equal or
reduced amount to the beneficiary for the remainder of their life.
Joint & Contingent Annuity with Period Certain An
annuity payable to a participant and beneficiary in a certain amount until the later
of (1) the death of the participant, or (2) the passage of a fixed
period of time, and payments continue in an equal or reduced amount to the
beneficiary for the remainder of their life.
Standard Method Benefit
payments are discounted using a constant interest rate for all payments in all
years. Segmented periods of time are not considered.
Select and Ultimate Method Benefit
payments are discounted using the designated interest rate over each segmented
period.
Pension Protection Act Method - Benefit
payments are discounted for ALL years using the interest rate for which the
payment is made during a segmented period.
qx probability
a person age x will die before age x+1
npx probability a person age x will
survive n years
lx number of
lives remaining at age x in a given mortality table computation
i annual
interest rate
v 1
1 + i
m frequency of payments in a year,
i.e., 12 denotes monthly
Dx vx lx
Nx ∑
Dx
N(m)x Nx [(m-1)/2m * Dx]
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Life Annuity |
δ(m)x |
= |
N(m)x Dx |
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Annuity Certain |
δ(m)n |
= |
1 - vn m[1 v(1/m)] |
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Annuity Certain and Continuous |
δ(m)x:n |
= |
δ(m)n + |
N(m)x+n Dx |
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Joint Annuity |
δ(m)x:y |
= |
N(m)x:y Dx:y |
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Joint Annuity with Period Certain |
δ(m)x:y:n |
= |
δ(m)n + |
N(m)x+n:y+n Dx:y |
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Joint & Survivor Annuity |
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P * (δ(m)x + δ(m)y) + (1-2P) *
δ(m)x:y where P is the survivor % |
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Joint & Survivor Annuity with Period Certain |
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δ(m)n |
+ P * ( |
N(m)x+n Dx |
+ |
N(m)y+n Dy |
) + (1-2P) * |
N(m)x+n:y+n Dx:y |
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where P is the survivor % |
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Joint & Contingent Annuity |
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δ(m)x + P * (δ(m)y - δ(m)x:y ) where P is the survivor % |
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Joint & Contingent Annuity with Period Certain |
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δ(m)n |
+ |
N(m)x+n Dx |
+ P * ( |
N(m)y+n Dy |
- |
N(m)x+n:y+n Dx:y |
) |
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where P is the survivor % |
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Curtate Expectation of Life |
ex |
= |
∑ npx = px + 2px + 3px + . . . . |
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Joint Curtate Expectation of Life |
exy |
= |
∑ npxy = pxy + 2pxy + 3pxy + . . . . |
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To apply Scale AA to produce the mortality rate for
years after 2000 use the following formula:
For non-annuitant rates:
qx2000+n = qx2000 * (1 - AAx)n+15
where AAX = annual improvement
factor in the mortality rate at age x.
For annuitant rates:
qx2000+n = qx2000 * (1 - AAx)n+7
where AAX = annual improvement
factor in the mortality rate at age x.