Ray's New Higher Arithmetic · Arts. 333–334 · Unit 22: Percentage with Time: Compound Interest and Annuities

96. Compound interest

Goal: Your student finds the compound amount and compound interest for yearly, half-yearly or quarterly intervals.

⏱ 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
  • A calculator, for checking only (optional)

What's in the book

Section VIII, Compound Interest: definitions, a comparison with annual interest, Case I with a worked problem, remarks on quarterly and true rates, a rule, and examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: $100 earns 10% a year. If the interest is added each year, how much after 2 years? ($121.)

  2. The idea

    Read:

    Compound Interest is interest computed both upon the principal and upon each accrued interest as additional principal.

    The final amount in Compound Interest is called the compound amount.

  3. The book's comparison

    Read the book's example: $1000 at 6% grows to $1060, then $1123.60, then $1191.016 in three years. On annual interest it would be $1190.80. The difference, $.216, is interest earned on interest.

  4. Work the book's problem

    Find the compound amount of $1000, in 4 years, at 2% per annum.

    Multiply by 1.02 four times: $1082.43216.

  5. The rule

    Read:

    To find the compound interest, deduct the original debt from the compound amount.

    For part of an interval, the book adds simple interest for the leftover months.

  6. Guided practice

    The compound amount of $1000, for 3 yr., at 10%, payable semi-annually.

    Half-yearly at 10% means 5% every 6 months, six times.

  7. Independent practice and wrap-up

    Your student works the other examples and checks the printed answers. Ask: Why does money grow faster when interest is compounded more often?

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