Life Essays
39 articlesEqual instalments versus equal principal: a month-by-month comparison on a 1M, 30-year loan
On a 1,000,000 principal over 30 years, this note compares equal-instalment and equal-principal repayment at 3.0% and 3.5%: monthly payment, total interest, monthly decrease, which period the cumulative totals cross at, and how much a 20-year term saves.
What you actually take home from a 10,000 yuan salary: thresholds, brackets and quick deductions
How much tax comes out of a 10,000 yuan monthly salary? Using a 5,000 yuan standard deduction, this note works through the seven progressive brackets, the quick-deduction recurrence and cumulative withholding, and explains why the number does not match your payslip.
Fraction addition and subtraction: seeing every step of the common denominator
When tutoring fraction addition, where the common denominator comes from, when to reduce, and why mixed numbers do not take part: this note works through 3/4+5/6 and 5/8-1/6 step by step on both routes.
Calculating the Chinese sexagenary cycle: zodiac years and ganzhi days
Ganzhi years and zodiac signs often disagree because there are two new-year boundaries: the start of spring and Spring Festival. This note verifies the modulo formula year by year, explains why the 60-year cycle repeats, and rechecks the anchor and general formula for ganzhi days.
Days until Chinese New Year: how holiday countdowns are calculated
Lunar holidays move on the Gregorian calendar every year, and the day difference has two conventions: inclusive or exclusive of today. This note uses a seven-year table from 2024 to 2030 to show the range and gaps for Spring Festival, Mid-Autumn and Double Ninth, and explains why the countdown can differ by a day.
How many teams can you form? Permutations versus combinations
Choosing 4 people from 12 for a duty roster gives 495 or 11,880, and the only difference is whether order counts. This note records a swap test for deciding, step-by-step verification of A and C, missed cases in repetition and at-least problems, and the first question to ask when factorials exceed the safe integer limit.
Chinese kinship terms: naming the son of the paternal aunt
Forgetting how to address a relative at New Year usually means the relationship chain was not unpacked: the older male cousin of my mother is a biaoju, not a biaoshu. This note gives a rule for tang versus biao (the son of the paternal aunt is a biaoge), explains that it only covers same-generation blood relatives, why titles are not symmetric, regional variation and when the terms apply.
How many calories do you burn a day? Calculating BMR
Six weeks of fat loss with no movement on the scale usually is not a willpower problem but an unclear basal metabolic rate. This note covers the relationship between BMR and TDEE, a step-by-step comparison of two common formulas, why activity multipliers get overestimated, and how much to eat once the number is known.
Adding pinyin to Chinese text: conversion with tone marks
Adding pinyin to a classical poem for a child, the hard part is pronunciation, not layout: the character for plant in one line reads zhòng, not zhǒng. This note covers where the tone mark goes, when ü drops its dots, tone sandhi versus original tones, and how to check characters with four readings, surnames, place names and the GB/T 28039 romanisation convention.
Counting words and characters for papers and copy: characters, lines, paragraphs
Word count in submission guidelines means at least four things: Chinese characters, words, characters including spaces, and characters excluding spaces. This note compares all four on the same sentence, shows which count spaces actually inflate, why soft returns and combining marks make numbers disagree, and gives pre-submission checks.
Many photos into one image: grid and heart-shaped collages
Turning more than 200 family photos into one image takes time mostly in selecting and deciding what to show. This note covers choosing a layout by photo count (2x2 is four-up, and the nine-grid layout means 3x3), unifying orientation, gap and radius values, the pixel budget before printing, and three things to check again.
What BMI counts as overweight? Calculating body mass index against Chinese adult standards
A health report labels BMI 28.8 as obese, while the same height and weight count only as overweight under international cut-offs. This note uses China standard WS/T 428-2013 for adult weight to explain the thresholds, how to work back to the normal range, and why waist circumference deserves attention before BMI.