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.
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.
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 |
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N(m)x Dx |
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Annuity Certain |
δ(m)n |
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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.