Life annuities may be either temporary life annuities or
whole life annuities. Both kinds have many practical uses in actuarial
calculations. In a temporary life annuity, each payment is made only if a
designated person is then alive, but the payments are limited to a fixed number
of years. In a whole life annuity, the payments continue for the entire
lifetime of a designated person.
There are also temporary life annuities in which the first
payment is made at the beginning, that is, on the same date on which the
present value is calculated. These are known as temporary life annuities due. The use of the word “due” is
comparable to its use in annuities certain. This type of annuity is important
in life insurance calculations, because premiums payable for a life insurance
policy represent an annuity due.
The line diagram of two five payments life annuities, one
immediate and one due, look like this:
To Illustrate: Using the given table
and 5% interest, calculate the present value at age 30 of a three – year life
annuity due of $100 per year.
Age
(x)

lx

30

9480358

31

9460165

32

9439447

33

9418208

Solution:
The line
diagram for this life annuity due appears as follows:
$ 100 $ 100 $ 100
^{Temporary
life annuity due} *
Age 30 31 32 33
The
expression for the present value will have a numerator representing the total
to be paid out to the survivors at each age with each such amount being
discounted at interest to the evaluation date. The first payment is due upon
the evaluation date. Hence, its present value is simply $100 (l30); it is not multiplied
by any discounting factor. The denominator is the number living at the
evaluation date:
Basic
equation:
Present
Value = $ 285.35
The
present value of annuity immediate of the same question must be less than the
present value of the life annuity due ($285.35), because each payment in the
annuity immediate is paid one year later than its counterpart in the annuity
due. Hence, there is a smaller probability that it will have to be paid, and
there are a greater number of years in which interest is earned.
To Illustrate:
Calculate the present
value at age 65 of a four year temporary life annuity due of $50 per year? (Use
given table and 6% interest)
Age (x)

lx

65

9019487

66

8935696

67

8847340

68

8753363

69

8652385

Solution:
The
line diagram for this life annuity due appears as follows:
$ 50 $ 50 $ 50 $ 50
_______________________________________________
Age 65 66 67 68 69
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ReplyDeleteLifetime annuities are great investments, especially for retirement. The idea is that you have this steady flow of cash monthly when you enter retirement. This is great because it helps you budget when you need to most. Maintaining money through retirement can be tricky but a long term annuity can help.
ReplyDeleteJeff
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ReplyDelete_______________________________________________________
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