Notesale: Turn your study into money

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Pension
Actuarial liability for pension benefits
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Let 𝛼
be the proportion, and let TPE be total pensionable earnings, the sum of salaries for all years of
service
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Then the annual pension is 𝛼𝑇𝑃𝐸
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1
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2
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𝐶𝑡 = 𝑣 1𝑝𝑥00 𝑡+1𝑉 − 𝑡𝑉 + 𝐸𝑃𝑉 (𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑝𝑎𝑖𝑑 𝑓𝑜𝑟 𝑚𝑖𝑑 𝑦𝑒𝑎𝑟 𝑒𝑥𝑖𝑡𝑠)
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PUC: projected unit credit (if the actuarial liability is calculated with the projected unit method)
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Then the normal contribution = 0𝑉 (𝑛)
Retiree Health Benefits
Expected present value
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𝑎𝐵 (𝑥, 𝑡): the benefit premium annuity
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𝐵(𝑥+1,𝑡)
𝐵(𝑥,𝑡+1)
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∞

𝑎̈ 𝐵 (𝑥, 𝑡) = ∑ 𝑣 𝑘 𝑘 𝑝𝑥 𝑐 𝑘 (1 + 𝑗)𝑘
1

∗

𝑘=0
1+𝑖

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Let 1 + 𝑖 = 𝑐(1+𝑗)
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AVTHB: actuarial value of total health benefits
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If we assume constant
rate of increase in health costs by age and time, then
𝐵(𝑥, 0)
𝑣 𝑡 𝐵(𝑥 + 𝑡, 𝑡) = 𝐵(𝑥, 0)𝑣 𝑡 𝑐 𝑡 (1 + 𝑗)𝑡 =
1 + (𝑖 ∗ )𝑡
65−𝑥

𝐴𝑉𝑇𝐻𝐵 = 𝐵(𝑥, 0) ∑

-

𝑖=0

1

∗

𝑟𝑥+𝑡 ∗ 𝑡
(𝑣 ) 𝑎̈ 𝑥+𝑡|𝑖 ∗
𝑙𝑥

Where 𝑣 =
1+𝑖 ∗
If we assume retirements occur in the middle of the year of age x+t, then the sum would have
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𝑣 𝑡+2 𝑎̈ 𝑥+𝑡+1|𝑖∗ instead of 𝑣 𝑡 𝑎̈ 𝑥+𝑡|𝑖 ∗
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APBO and Normal cost
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The normal cost is defined the same way as it is for pension benefits:
𝑛𝑜𝑟𝑚𝑎𝑙 𝑐𝑜𝑠𝑡 = 𝑣𝑝𝑥 1𝑉 + 𝐸𝑃𝑉(𝑒𝑥𝑖𝑡 𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠) − 0𝑉
3
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