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Unformatted text preview: th a 2-year policy, Premium in year 1 > $275
Essentially, pre Premium in year 2 < $298
funding costs With this example, size of difference is small With whole life policies (UL) Difference can be large
Gives rise to cash value Annuities Annuity Contracts Large and growing part of life insurance business Risk management perspective Protection against outliving resources Saving Perspective Tax advantaged method of saving Implicit returns are tax deferred How do you fund an annuity? Divide contract period in two Accumulation period where the Policyholder pays premiums
Payout period where the Insurer makes payments
If payout period begins upon purchase of contract, this is an
If there is an accumulation period prior to the payout period,
these are deferred annuities.
these Payments may be made: All at once (single premium)
Over time Fixed payments OR
Flexible Payments Payout Period of Annuities Straight life (or life annuity) Annuity Certain (or Term Certain) Life annuity with period certain (or Term
Life certain and life thereafter) Joint and last survivor
End at death of two people Payment may be reduced after death of
first. Savings Feature Fixed annuities Two types of variable annuities Return credited varies with investment
returns, however, insurer guarantees a
minimum Return credited varies with return on
assets chosen by contract holder, no
guarantee may exist
guarantee Pricing Immediate Annuities Example: Find single premium for a $5,000
Example: life annuity for a 96 year old
life Assume person dies by age 100 Interest rate = 10% Premium = PV of expected payments to
Premium annuitant = $4,530
annuitant Probability of a 96 year-old surviving to Age x
= # alive at age x/# alive at 96.
alive Pricing Immediate Annuities
Probability of a
surviving Expected Payment
$5000 x prob. PV of Expected Payment 6050/9831 $3,077 $3,077 / 1.1 = $2,797 3145/9831 $1,600 $1,600 / 1.12 = $1,322 1076/9831 $547 $ 547 / 1.13 = $ 411 0 0 0...
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