This worksheet has been designed and tested using Netscape 3.0. It should work with later versions of Netscape's browsers but will not work with other browsers. It uses only JavaScript for computations and should cause no problems when used with the appropriate browsers. The operative word here is "should" -- the author cannot guarantee fault-free operation.

You should be able to use the worksheet when not connected to
the internet. Save the program file (ws_***.htm) and the
accompanying instruction file (wi_***.htm) on your disk using the
browser's command to **F**ile **S**ave.
At a later time you may retrieve the file using the browser's **F**ile
**O**pen file command; you may then use the page as
you would if you were on the network. Note, however, that the
file saved will have all the initial settings rather than those
you have changed.

When using the worksheet, you may change any inputs. To do so, click inside the appropriate box, then make your changes or select the desired radio buton. When finished, click any area outside the boxes on the form.

This worksheet is designed to find the present value of a **fixed
annuity**.** **It** **is not
suitable for valuing an annuity involving payments that vary with
investment performance.

All inputs are contained in the table. The worksheet may be
used for a **joint annuity** covering a worker and a
beneficiary, or for a **single annuity** covering
only a worker. In either case, data must be provided for a **worker.
**For joint policies information must also be provided for
the beneficiary. If a single annuity is chosen, any beneficiary
information will be ignored.

The key terms of the annuity are provided in an **Amount
paid** block. Only the one applicable for the chosen type
of policy (single or joint) will be used. Amounts entered may be
nominal or real. They may be actual amounts (for example, 10,000)
or relative (for example, 1.0 if both are alive and 0.5 if only
one is alive). To aid readability, commas may be included in
numbers entered in these boxes (they will be removed when the
entry is processed).

The values for the amounts paid values are used for the first
year in which payments are made. In each subsequent year these
amounts are increased by the percentage specified in the box for **Growth
rate in amount paid** (for example, enter 3.50 for 3.50%
per year). If a constant annuity is desired, enter zero in this
box. If the annuity is to begin immediately, enter zero in the **Years
deferred** box. For a deferred annuity, enter the number
of years before the first payment is to be made.

Two sets of mortality tables, taken from the *Life
Insurance Fact Book*, are provided. The first is the
Commissioners 1980 Standard Ordinary (1970-1975) table, designed
for estimating mortality for those who apply for individual life
insurance policies. The second is the 1983 Individual Annuity
Table (1971-1976, projected to 1983), designed for estimating
mortality for those who apply for individual annuity policies.
According to the Fact Book:

"Mortality rates contained in the 1980 Commissioners Standard Ordinary Table were obtained from experience of 1970-1985, but contain an added element designed to generate life insurance reserves of a conservative nature in keeping with the long-term guarantees inherent in life insurance contracts.... Mortality rates for the 1983 Individual Annuity Tables are, again, conservative as related to the actual and projected experience on which they are based."

Five mortality assumption choices are provided. Either of the two tables can be used. Alternatively, a combination of the two can be selected. In the latter case, the death rate per 1,000 individuals of any given age and sex is computed by taking a weighted average of the corresponding figures from the two tables. For a typical individual, a 0.50/0.50 combination of the two tables may be the most appropriate choice. For a joint annuity, a selection must be made for both the worker and the beneficiary. For a single annuity, the latter information is ignored.

The final input concerns the **Annuity discount rate**.
This should be stated as an annual percentage rate (for example,
6.00 for 6.00% per year). All expected cash flows are discounted
to the current date at this rate. If payments are nominal amounts
an appropriate nominal rate of interest should be utilized. On
the other hand, if the payments are real (that is, of constant
purchasing power), a real rate of interest should be employed.

The worksheet computes the expected amount paid in each year, then discounts these amounts back to the present, using the assumed discount rate. The death rate for each age is taken as the probability that an individual of that age will die within the next 12 months (and hence live for 0.50 years). Expected values are based on the probabilities of the possible states of the world each year, along with the associated payments. State probabilities take into account the transition probabilities from each possible state to each of the other possible states, using the probabilities of death for the worker and (where applicable), the beneficiary.

When you wish to find the present value of the annuity
described in the table, click the **PROCESS**
button. The present value will appear in the box to the right of
the button. The amount is stated in units of currency as of the
current date (that is, the date at which the worker's age is that
shown in the upper left-hand box in the table).