Annuity

A contract that converts savings into a stream of payments, often used to manage retirement income and longevity risk.

An annuity is a contract that turns a lump sum or accumulated balance into a stream of payments over time. It matters economically because it helps households smooth consumption and, in the case of life annuities, insure against the risk of outliving their savings.

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Why Annuities Matter

A household planning for retirement faces a difficult problem: it does not know exactly how long it will live. If it spends too quickly, it may run out of money. If it spends too cautiously, it sacrifices current consumption unnecessarily. A life annuity partly solves that problem by pooling longevity risk across many people.

Pricing Intuition

A simplified present-value relationship is:

[ P \approx \sum_{t=1}^{T} \frac{s_t C}{(1+r)^t} ]

where P is the premium, C is the periodic payment, r is the discount rate, and s_t is the probability that the annuitant is still alive at time t. Higher interest rates tend to support higher payouts, while longer expected lifetimes tend to reduce them.

Main Types

Common annuity types include:

  • immediate versus deferred annuities
  • fixed versus variable annuities
  • term-certain versus life annuities
  • inflation-protected or joint-and-survivor contracts

Each design trades off income stability, flexibility, and protection against longevity risk.

The Annuity Puzzle

Standard life-cycle theory often predicts more annuity demand than is observed in practice. Economists explain the gap with factors such as bequest motives, liquidity concerns, complexity, adverse selection, and distrust of providers.

Knowledge Check

### What problem does a life annuity help solve? - [x] The risk of outliving one's savings - [ ] The problem of measuring GDP - [ ] The need to eliminate all taxes - [ ] The challenge of pricing exports > **Explanation:** Life annuities provide income while the annuitant remains alive, which helps manage longevity risk. ### Why can a life annuity pay more than a self-managed drawdown with the same investment return? - [ ] Because annuities never charge costs - [x] Because mortality pooling creates longevity insurance and mortality credits - [ ] Because annuities remove interest-rate risk entirely - [ ] Because annuities are always subsidized by the government > **Explanation:** People who die earlier leave funds in the risk pool, which supports payments to those who live longer. ### What is one reason households may buy fewer annuities than simple models predict? - [ ] Because retirement income is irrelevant - [x] Because bequest motives, liquidity needs, and complexity can reduce demand - [ ] Because annuities never provide fixed payments - [ ] Because everyone knows their exact lifespan > **Explanation:** The so-called annuity puzzle reflects frictions and preferences that make households less willing to annuitize wealth fully.