Ray's New Higher Arithmetic · Arts. 270–273 · Unit 16: Percentage: Applications without Time (continued)

73. Stock investments: Cases II to V

Goal: Your student finds the dividend rate, the amount to invest, the rate of income, and the market price that gives a wanted rate of income.

⏱ About 45 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

Case II (rate of dividend), Case III (amount invested), Case IV (rate of income) and Case V (market value), each with a worked problem and examples. Most answers are printed.

The lesson, step by step

  1. Warm-up

    Review Case I: $1900 invested in 6% stock at 95. ($1900 ÷ .95 = $2000 par; income $120.)

  2. Case II: the dividend rate

    Invested $10132.50 in railroad stock at 105%, which pays me annually $965: what is the rate of dividend on the stock?

    $10132.50 ÷ 1.05 = $9650 of par; $965 ÷ $9650 = 10%.

  3. Case III: how much to invest

    If U. S. bonds, paying 5% interest, are selling at 108½%, how much must be invested to secure an annual income of $2000?

    $2000 ÷ .05 = $40000 of par; at 108½% it costs $40000 × 1.085 = $43400.

  4. Case IV: rate of income

    What per cent of his money will a man realize in buying 6% stock at 80%?

    Each 80 cents buys $1 of stock paying 6 cents: $.06 ÷ $.80 = 7½%.

    Try together:

    What is the rate of income on Pacific Mail 6's, bought at 30?

  5. Case V: the right price

    Read the book's solution:

    What must I pay for Lake Shore 6's ($100 a share), that the investment may yield 10%?

    If bought for $100, or par, it will yield 6%; to yield 1% it must be bought for $100 × 6 = $600; to yield 10% it must be bought for 1/10 of $600 = $60.

  6. Independent practice

    Your student picks two examples from each case. Include Case V, Example 2 (the one without a printed answer):

    Which is the best permanent investment: 4's at 70%, 5's at 80%, 6's at 90%, or 10's at 120%? Why?

  7. Wrap-up

    Ask: Which pays more on your money, 6% stock bought at 80 or bought at 120? (At 80: 7½% against 5%.)

Afterwards

This is a big lesson. Split it: Cases II and III one day, Cases IV and V the next.

Answers to the book's problems

Case V, Ex. 2 (no printed answer): rate of income = dividend ÷ price. 4's at 70: 5 5/7%; 5's at 80: 6¼%; 6's at 90: 6⅔%; 10's at 120: 8⅓%. The 10's at 120% are the best, because they pay the most on the money invested.

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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