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LA 2100 · Quadrivium: The School of Arithmetic — Module 7: Percentage, Profit and Loss, and Interest

Led by James B. Thomson Simulacrum

1 modules 8 tutorials · ~10 hours Mathematics Updated today

Five commercial names for one method. Percentage, profit and loss, commission, insurance and interest as a single relation between base, rate and result — with time as the only genuinely new element.

Percentage, Profit a…7
  1. Module 7

    Percentage, Profit and Loss, and Interest

    Led by James B. Thomson Simulacrum

    The question

    Eight sittings, Thomson's pages 193 to the end, and the last of the

    Outcome

    The student can express any rate as a common fraction and as a

    Sub-units

    1. 7.1 Per Cent Is a Fraction With a Fixed Denominator
    2. 7.2 Base, Rate, Percentage: The Three Cases
    3. 7.3 Profit and Loss
    4. 7.4 Commission, Insurance, and the Naming of Things
    5. 7.5 Interest: The One New Element
    6. 7.6 Simple Interest for Years, Months and Days
    7. 7.7 Analysis in Commercial Problems
    8. 7.8 Review of the Whole School

    Practice scenarios

    The Two Merchants

    Two merchants have each sold goods for the same sum and each claims a twenty per cent margin. The first computed his twenty per cent on what the goods cost him. The second computed his on what he sold them for. They have made different amounts of money and neither can see why, since both did the arithmetic correctly and both used twenty per cent. A third party is now trying to compare their businesses using the figures they have supplied.

    Your goals

    • Identify which quantity each merchant used as his base
    • Compute the actual gain in each case and show the difference
    • Say which is using "margin" as trade normally does, and which means "markup"
    • State what the third party must ask for before the figures can be compared
    • Decide whether either merchant has done anything dishonest