Ray's New Higher Arithmetic · Arts. 254–256 · Unit 16: Percentage: Applications without Time (continued)

68. Premium and discount: words and Case I

Goal: Your student explains par value, market value, premium and discount, and finds the premium or discount and the cost of stocks, drafts and money.

⏱ About 40 minutes · 8 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

Section III, Premium and Discount: definitions (drafts, par value, market value, discount, premium, rate), the four cases matched to percentage, and Case I with fourteen examples. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: A $5 bill is worth $5. Could a piece of paper that says "$100" ever sell for more or less than $100? When?

    Let your student guess. Then say that this lesson is about exactly that.

  2. The idea

    Read the definitions together:

    The Par Value of money, stocks, drafts, etc., is the nominal value on their face.

    The Market Value is the sum for which they sell.

    Discount is the excess of the par value of money, stocks, drafts, etc., over their market value.

    Premium is the excess of their market value over their par value.

    SayPar is the printed value. If it sells above par, the extra is a premium. If it sells below par, the shortfall is a discount.

  3. Old money words

    In 1880 a draft (a written order to pay money at another place) and "uncurrent money" (bank notes from a distant or shaky bank) often sold above or below face value. Gold also had a premium over paper money. The book's problems use all of these.

  4. Work the book's example

    The four cases work like percentage. The par value is the base, and the premium or discount is the percentage. Work Example 1 together:

    Bought 54 shares of railroad stock ($100 each) at 4% discount: find the discount and cost.

    Par = 54 × $100 = $5400. Discount = $5400 × .04 = $216. Cost = $5400 − $216 = $5184. Check the printed answer.

  5. Guided practice

    Do these two together, out loud:

    What is a $5 note worth, at 6% discount?

    Sold $425 uncurrent money, at 3% discount: what did I get, and lose?

    For each, first ask: Is it above par or below? Should we add or subtract?

  6. Independent practice

    Your student works the rest of the Case I examples. Have them write par, rate and premium or discount in a short column before multiplying.

  7. Check

    Compare with the printed answers. If an answer is off, check whether the premium was added or the discount subtracted.

  8. Wrap-up

    Ask: Is the rate of premium or discount figured on the par value or on the market value? (On the par value, the face.)

Afterwards

Next day, re-do any missed examples. Then go on to Cases II to IV.

Tip

Keep a running card of the new words (par, market value, premium, discount, draft). They come back in every lesson until interest.

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