Ray's New Higher Arithmetic · Arts. 300–301 · Unit 17: Percentage with Time: Interest

81. Finding the principal

Goal: Your student finds the principal from the interest, or from the amount.

⏱ About 35 minutes · 6 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

Case IV (from interest, rate and time, find the principal) and Case V (from amount, rate and time, find the principal), each with a worked problem, a rule and examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: What sum earns $6 a year at 6%? ($100.)

  2. Case IV

    Read:

    Given the interest, rate, and time, to find the principal.

    A man receives $490.84 interest annually on a mortgage, at 7%: what is the amount of the mortgage?

    $490.84 ÷ .07 = $7012.

    Multiply the rate by the time, and divide the interest by the product; the quotient will be the principal.

  3. Case V

    Read:

    Given the amount, rate, and time, to find the principal.

    What is the par value of a bond which, in 8 yr. 8 mo., at 6%, will amount to $15200?

    In 8 yr. 8 mo. at 6%, $1 grows to $1.52. $15200 ÷ 1.52 = $10000.

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

  4. Guided practice

    Together:

    What principal in 2 yr. 3 mo. 12 da., at 6%, will amount to $1367.84?

    What principal, at 4½%, will amount to $4613.36 in 3 yr. 1 mo. 7 da.?

  5. Independent practice

    Your student works the remaining examples from both cases.

  6. Check and wrap-up

    Check the printed answers. Ask: Why can't we just subtract 6% from $15200? (Because the interest was figured on the principal, not on the amount.)

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