10217

# Net and Gross Reserve of Life Insurance

This Demonstration shows the net and gross premium reserves of life insurance. The reserves are calculated for the three basic types of life insurance: term insurance, pure endowment, and endowment with unitary benefit. For all cases, the premium can be paid as an -year temporary annuity. You can vary the technical interest rate in the range from 1 to 10% per annum. The decremental data used for the calculations is 2001–2005 Czech Republic data.

### DETAILS

Term life insurance is the basic insurance product where the insurance event is the death of the insured. For pure endowment, the insurance event is the survival of the term. The endowment is a mixture of the two other types of insurance.
The net reserve of endowment for years, where the premium is paid in years, is:
( is used for the more standard actuarial notation.)
Assuming the initial costs to be of the benefit, the administrative costs of the benefit, and the collection fee of the gross premium (but as follows the result does not depend on ), we can calculate the gross premium as
,
then the gross reserve is
where
is the net reserve in time ,
is the gross reserve in time ,
is the endowment for years,
is the annual premium paid within years.
The calculation of reserves for term insurance and pure endowment is analogous, using for term life insurance and for pure endowment.
The computation is based on the commutation functions:
,
,
where , , and can be derived using the decremental data and :
and ,
and ,
where
.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.