Reading Numbers and Documents

P2　—　How much can you trust numbers?

Nominal and real, ratios and denominators, compound interest and fees. Learn how to read numbers and become able to read statements, contracts, and official documents on your own.

Supervised by: Mitsuru Hayama　／　Reading time (main text): About 8 min (4,034 characters of text at 500 chars/min; exercises and readings not included)　／　Beyond the text: 6 exercises · 2 coins · 3 readings

What this course teaches you to do

• Can distinguish between nominal and real values, and can personally calculate the erosion of real value using the inflation rate.
• Can verify the denominator of a ratio and question the original number behind terms like "double," "half," and "%".
• Can place simple and compound interest, fees, and interest rates into a single formula, and can calculate the difference after ten years using one's own numbers.
• Has a method for reading statements, contracts, and official documents, and can state where to seek clarification for unfamiliar sections.

Lessons (8)

1. Numbers Have Three Accompaniments — Point in Time, Unit, and DenominatorTime point, unit, denominator. A number that lacks even one of these three is not yet a number.
2. Nominal and Real — The Lesson of the IchibuginNominal is the paper value; real is how much you can buy now. Nominal ÷ (1 + inflation rate)^years.
3. The denominator of a ratio — What is the basis for "double"?State the denominator and period for ratios. Differences are in points, ratios are in %.
4. Simple and Compound Interest — Putting a Price on TimeSimple interest is on the principal only; compound interest is also on the interest. Principal × (1 + annual rate) ^ number of years. Even a small difference in rates leads to a large difference in the amount over the years.
5. Fees are an invisible priceFees compound. 1 − (1 − rate)^years. Add the fees for buying, holding, and exiting into a single rate.
6. Questioning the graph — Axes, period, units, sourceA graph is a picture. Trust its direction only after checking four things: the vertical axis, the time period, whether it is nominal or real, and the source.
7. The order for reading statements and contracts — total amount, period, cancellation, fees, counterpartyTotal amount, period, cancellation, fees, counterparty. Reading in this order helps you understand the overall weight before getting lost in the details.
8. Reading official documents — Using a pension notice as an exampleWhat kind of document is it? Which format applies? Are the values nominal or real? Are there any errors? Where can it be verified? The procedure is the same, regardless of the country.

Readings (3)

• Before the beginning　Overview: 2,700 years of the world　2000 BC　Babylonia
  A world where numbers always had a unit: "X grams of silver". Numbers without units did not exist.
• The black ships and the outflow of gold　Japan　1858　Shimoda, the American consulate
  A sentence from a treaty that mixed the world of weight with the world of face value. The first lesson on nominal versus real value.
• When temples were banks　Japan　the 7th–13th centuries　The granaries of the provinces
  The interest rate on a temple loan. An example of the price of time exceeding the principal within a year.

Assessment

6 exercises in this course (4 check, 0 compare, 2 written). Progress is recorded by self-assessment.