"Sun Tzŭ's Computational Classic: Volume III" 《孫子算經卷下》 §13

《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§13. Discounting by a rate (2)

This section gives a worked example of discounting a quantity by rates.

The relevant unit conversions for capacity are

\begin{aligned} 1 \unit{barrel~(斛)} &= 10 \unit{pecks~(斗)} \\ 1 \unit{peck~(斗)} &= 10 \unit{quarts~(升)} \\ 1 \unit{quart~(升)} &= 10 \unit{gills~(合)}. \end{aligned}

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text	Target text	Notes
今有粟三十六萬九千九百八十斛七斗、在倉九年、年斛耗三升。	Suppose there be grain thirty-six myriad nine thousand nine hundred [and] eighty barrels [and] seven pecks, [stored] in [a] granary nine years, [and each] year [for each] barrel [there be] expended three quarts.
問一年九年各耗幾何。	[We] ask, how much [be] expended [for] each of one year [and] nine years?
答曰、一年耗一萬一千九十九斛四斗二升一合、九年耗九萬九千八百九十四斛七斗八升九合。	Answer saith: [for] one year [there be] expended one myriad one thousand [and] ninety-nine barrels, four pecks, two quarts, [and] one gill; [and for] nine years [there be] expended nine myriad nine thousand eight hundred [and] ninety-four barrels, seven pecks, eight quarts, [and] nine gills.
術曰、置三十六萬九千九百八十斛七斗、以三升乘之、得一年之耗。	Method saith: put [down the] thirty-six myriad nine thousand nine hundred [and] eighty barrels [and] seven pecks; multiplying it by [the] three quarts, resulteth in [the] expense of one year.
又以九乘之、即九年之耗。	And multiplying it by nine, is [it the] expense of nine years.	In modern notation, \begin{aligned} & 369980.7 \unit{barrels} \times \frac{3 \unit{quarts} / {\unit{barrel}}}{\unit{yr}} \times (1 \unit{yr}, 9 \unit{yr}) \\[\tallspace] &= (11099.421 \unit{barrels}, 99894.789 \unit{barrels}). \end{aligned} Note that the nine-year expense is not compounded, but computed directly from the principal value.

Source text

Target text

Notes

今有粟三十六萬九千九百八十斛七斗、在倉九年、年斛耗三升。

Suppose there be grain thirty-six myriad nine thousand nine hundred [and] eighty barrels [and] seven pecks, [stored] in [a] granary nine years, [and each] year [for each] barrel [there be] expended three quarts.

問一年九年各耗幾何。

[We] ask, how much [be] expended [for] each of one year [and] nine years?

答曰、一年耗一萬一千九十九斛四斗二升一合、九年耗九萬九千八百九十四斛七斗八升九合。

Answer saith: [for] one year [there be] expended one myriad one thousand [and] ninety-nine barrels, four pecks, two quarts, [and] one gill; [and for] nine years [there be] expended nine myriad nine thousand eight hundred [and] ninety-four barrels, seven pecks, eight quarts, [and] nine gills.

術曰、置三十六萬九千九百八十斛七斗、以三升乘之、得一年之耗。

Method saith: put [down the] thirty-six myriad nine thousand nine hundred [and] eighty barrels [and] seven pecks; multiplying it by [the] three quarts, resulteth in [the] expense of one year.

又以九乘之、即九年之耗。

And multiplying it by nine, is [it the] expense of nine years.

In modern notation,
\begin{aligned} & 369980.7 \unit{barrels} \times \frac{3 \unit{quarts} / {\unit{barrel}}}{\unit{yr}} \times (1 \unit{yr}, 9 \unit{yr}) \\[\tallspace] &= (11099.421 \unit{barrels}, 99894.789 \unit{barrels}). \end{aligned}
Note that the nine-year expense is not compounded, but computed directly from the principal value.

《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III" §13. Discounting by a rate (2)

Translation

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《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§13. Discounting by a rate (2)