- Actuarial present value
actuarial science, the actuarial present value of a payment or series of payments which are random variables is the expected valueof the present valueof the payments, or equivalently, the present value of their expected values.
This applies to
life insurances, including life annuities. The result depends on age through life tables, and on the interest rate.
internal rate of returnof a contract is the rate of returnfor which the actuarial present value of all cash flows is zero.
Let be the future lifetime
random variableof an individual age x and be the present value random variable of a whole life insurancebenefit of 1 payable at the instant of death.
where "i" is the interest rate and δ is the equivalent
force of interest.
To calculate the actuarial present value we need to calculate the expected value of this random variable Z. For someone aged "x" this is denoted as in
actuarial notation. It can be calculated as
where is the
probability density functionof "T", is the probability of a life age surviving to age and "μ" denotes force of mortality.
The actuarial present value of an n-year term insurance policy can be found similarly by integrating from 0 to "n".
The actuarial present value of an n year pure endowment insurance benefit of 1 payable after n years if alive, can be found as
In practice the best information available about the random variable "T" is drawn from
life tables, which give figures by year. The actuarial present value of a benefit of 1 payable at the birthday after death would be
Wikimedia Foundation. 2010.
Look at other dictionaries:
Net present value — In finance, the net present value (NPV) or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity. In the case when… … Wikipedia
Actuarial notation — 1. net single premium of insurance (benefit 1 unit) 2. paid at the moment of death 3. for x year old person, for n years 4. life insurance 5. deferred (m year) 6. with double force of interestActuarial notation is a shorthand method to allow… … Wikipedia
Actuarial reserves — An actuarial reserve is a liability equal to the net present value of the future expected cash flows of a contingent event. In the insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the … Wikipedia
Actuarial Society of India — The Actuarial Society of India, known as the ASI Or Intstitute of Actuaries of India known as IAI, is the sole professional body of actuaries in India, and was formed in September 1944.Registration of the ASIIn 1979, it was admitted to the… … Wikipedia
Actuarial Equivalent — is generally used for applying some measurement to two benefit plans to see if the resulting values are sufficiently close. Often, two or more payment streams of the benefit plans end up having the same present value based on the actuarial… … Investment dictionary
Actuarial science — are professionals who are qualified in this field through examinations and experience. Actuarial science includes a number of interrelating subjects, including probability and statistics, finance, and economics. Historically, actuarial science… … Wikipedia
Actuarial topics — This page represents a collection of topics which relate to Actuarial Science.General Actuarial Topics* Actuarial science * Actuary * Actuarial notation * Fictional actuariesMathematics of Finance* Financial mathematics* Interest * Time value of… … Wikipedia
Actuarial Cost Method — A method used by actuaries to calculate the amount a company must pay periodically to cover its pension expenses. The two main methods used are the cost approach and the benefit approach. The cost approach calculates total final benefits based on … Investment dictionary
Actuarial Balance — The difference between future Social Security obligations and the income rate of the Social Security Trust Fund as of present. The Social Security program would be said to be in actuarial balance if the summarized income rate is inline with the… … Investment dictionary
Actuarial Deficit — The difference between future Social Security obligations and the income rate of the Social Security Trust Fund as of present. The Social Security program is said to be in actuarial deficit if the summarized income rate is less than the… … Investment dictionary