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Life annuity

Life annuity is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Life annuity rather than just read about it. In short: A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. The majority of life annuities are insurance products sold or issued by life insurance companies.

Key takeaways

  • Life annuity belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Life annuity to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Life annuity from memory before moving on to harder problems.

Reference excerpt

A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. The majority of life annuities are insurance products sold or issued by life insurance companies. However, substantial case law indicates that annuity products are not necessarily insurance products. Annuities can be purchased to provide an income during retirement, or originate from a structured settlement of a personal injury lawsuit. Life annuities may be sold in exchange for the immediate payment of a lump sum (single-payment annuity) or a series of regular payments (flexible payment annuity), prior to the onset of the annuity. The payment stream from the issuer to the annuitant has an unknown duration based principally upon the date of death of the annuitant. At this point the contract will terminate and the remainder of the fund accumulated is forfeited unless there are other annuitants or beneficiaries in the contract. Thus a life annuity is a form of longevity insurance, where the uncertainty of an individual's lifespan is transferred from the individual to the insurer, which reduces its own uncertainty by pooling many clients.

History The instrument's evolution has been long and continues as part of actuarial science. Ulpian is credited with generating an actuarial life annuity table between AD 211 and 222. Medieval German and Dutch cities and monasteries raised money by the sale of life annuities, and it was recognized that pricing them was difficult. The early practice for selling this instrument did not consider the age of the nominee, thereby raising interesting concerns. These concerns got the attention of several prominent mathematicians over the years, such as Huygens, Bernoulli, de Moivre and others: even Gauss and Laplace had an interest in matters pertaining to this instrument. It seems that Johan de Witt was the first writer to compute the value of a life annuity as the sum of expected discounted future payments, while Halley used the first mortality table drawn from experience for that calculation. Meanwhile, the Paris Hôtel-Dieu offered some fairly priced annuities that roughly fit the Deparcieux table discounted at 5%. Continuing practice is an everyday occurrence with well-known theory founded on robust mathematics, as witnessed by the hundreds of millions worldwide who receive regular remuneration via pension or the like. The modern approach to resolving the difficult problems related to a larger scope for this instrument applies many advanced mathematical approaches, such as stochastic methods, game theory, and other tools of financial mathematics.

Types

Defined benefit pension plans Defined benefit pension plans are a form of life annuity typically provided by employers or governments (such as Social Security in the United States). The size of payouts is usually determined based on the employee's years of service, age and salary.

Individual annuity Individual annuities are insurance products marketed to individual consumers. With the complex selection of options available, consumers can find it difficult to decide rationally on the right type of annuity product for their circumstances.

Deferred annuity There are two phases for a deferred annuity:

the accumulation or deferral phase in which the customer deposits (or pays premiums) and accumulates money into an account; the distribution or annuitization phase in which the insurance company makes income payments until the death of the annuitants named in the contract Deferred annuities grow capital by investment in the accumulation phase (or deferral phase) and make payments during the distribution phase. A single premium deferred annuity (SPDA) allows a single deposit or premium at the issue of the annuity with only investment growth during the accumulation phase. A flexible premium deferred annuity (FPDA) allows additional payments or premiums following the initial premium during the accumulation phase. The phases of an annuity can be combined in the fusion of a retirement savings and retirement payment plan: the annuitant makes regular contributions to the annuity until a certain date and then receives regular payments from it until death. Sometimes there is a life insurance component added so that if the annuitant dies before annuity payments begin, a beneficiary gets either a lump sum or annuity payments.

Immediate annuity An annuity with only a distribution phase is an immediate annuity, single premium immediate annuity (SPIA), payout annuity, or income annuity. Such a contract is purchased with a single payment and makes payments until the death of the annuitant(s).

Fixed and variable annuity Annuities that make payments in fixed amounts or in amounts that increase by a fixed percentage are called fixed annuities. Variable annuities, by contrast, pay amounts that vary according to the investment performance of a specified set of investments, typically bond and equity mutual funds. Variable annuities are used for many different objectives. One common objective is deferral of the recognition of taxable gains. Money deposited in a variable annuity grows on a tax-deferred basis, so that taxes on investment gains are not due until a withdrawal is made. Variable annuities offer a variety of funds ("subaccounts") from various money managers. This gives investors the ability to move between subaccounts without incurring additional fees or sales charges. Variable annuities have been criticized for their high commissions, contingent deferred sale charges, tax deferred growth, high taxes on profits, and high annual costs. Sales abuses became so prevalent that in November 2007, the Securities and Exchange Commission approved FINRA Rule 2821 requiring brokers to determine specific suitability criteria when recommending the purchase or exchange (but not the surrender) of deferred variable annuities.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Life annuity

Start with the simplest possible case. Write down what Life annuity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Life annuity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Life annuity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Life annuity

In research
Life annuity appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Life annuity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Life annuity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Actuarial science, Annuities, Retirement, so understanding it makes those chapters shorter.
In everyday life
Look for Life annuity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Life annuity in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Life annuity means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Life annuity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Life annuity in simple terms?

A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. The majority of life annuities are insurance products sold or issued by life insurance companies.

Why does Life annuity matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Life annuity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Life annuity.

Tags

  • Actuarial science
  • Annuities
  • Retirement

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