Ray's New Higher Arithmetic · Arts. 335–338 · Unit 22: Percentage with Time: Compound Interest and Annuities

97. Compound interest by tables, and Cases II to IV

Goal: Your student uses the book's table of compound amounts to find an amount, a time, a rate or a principal.

⏱ About 45 minutes · 7 steps

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You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil
  • A calculator, for checking only (optional)

What's in the book

Calculation by tables: two pages of tables of the amount of $1 at 2% to 10% for up to 55 years, how to use them, then Case II (find the time), Case III (find the rate) and Case IV (find the principal or present worth), with examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Look at the table together. Find the amount of $1 at 6% for 10 years. Ask: About how long does it take money to double at 6%?

  2. Using the table

    Read:

    When the intervals are many, the actual multiplications become laborious; and, therefore, tables of compound interest have been prepared to shorten the work.

    Try:

    Find the compound amount of $750 for 17 yr., at 6%, payable annually.

    Find 17 years under 6%, and multiply by 750.

  3. Case II: the time

    Work the book's problem: $750 to amount to $2000 at 8% payable half-yearly. $2000 ÷ $750 = 2.6667, the amount of $1 at 4% a half-year. The table gives 25 intervals, and a little more. The answer is about 12 yr. 6 mo.

  4. Case III: the rate

    At what rate will $1000 amount to $2411.714 in 20 years?

    Look along the 20-year row for 2.411714. Which column is it in?

  5. Case IV: the principal

    Read:

    Divide the given interest or amount by the interest or amount of $1 for the given time and at the given rate; the quotient will be the required principal.

    Try:

    What principal, at compound interest, will yield $52669.93 in 25 yr., 6%?

  6. Independent practice

    Your student works one or two examples of each case and checks the printed answers. A calculator may be used for checking.

  7. Wrap-up

    Ask: What is the difference between "present worth at compound interest" and true discount from Lesson 1019? (One uses compound interest, the other simple.)

Afterwards

This is two days' work: the table and Case II, then Cases III and IV.

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