Ray's New Higher Arithmetic · Arts. 348–353 · Unit 22: Percentage with Time: Compound Interest and Annuities

100. Life annuities, dowers and reversions optional

Goal: Your student uses the life-annuity table to value an annuity on a person's life, a life-estate or a dower, and its reversion.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Contingent annuities: expectation of life, the Carlisle table of mortality, a table of single-life annuities at 4% to 7%, and three cases (value of a life annuity, size of annuity a sum will buy, value of a reversion), with examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: Would an insurance company pay more for a promise of $100 a year to a 20-year-old or to a 70-year-old? Why?

  2. The idea

    Read:

    Contingent Annuities comprise Life Annuities, Dowers, Pensions, etc.

    The value of such annuities depends upon the expectation of life.

    Expectation of Life is the average number of years that a person of any age may be expected to live.

  3. The tables

    Look at the Carlisle mortality table (it follows 10,000 people from birth) and the life-annuity table. Then read:

    The preceding table of life annuities shows the sum to be paid by a person of any age, to secure an annuity of $1 during the life of the annuitant.

  4. Case I

    Read:

    Find from the table the value of a life annuity of $1, for the given age and rate of interest, and multiply it by the payment of the given annuity.

    Try:

    What must be paid for a life-annuity of $650 a year, by a person aged 72 yr., int. 7%?

  5. Dowers and reversions

    The book explains a widow's dower as a life-estate in one third of her husband's real estate. A reversion is what is left after the life-estate ends. Try:

    What is the life-estate and reversion in $25000, age 55 yr., int. 6%?

  6. Cases II and III

    Read the Case II rule:

    Assume $1 a year for the annuity; find from the table its value for the given age and rate of interest, and divide the given cost by it; the quotient will be the payment required.

    Your student works one example of each case.

  7. Check and wrap-up

    Check the printed answers. Ask: Why are the table values smaller for older ages?

Tip

The dower law described here is 1880 law and has long since changed. This lesson can be skipped or done lightly.

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