Abstract
In Sanskrit legal texts, much space is devoted to the subject of loans and interest. Moreover, almost all Sanskrit mathematical texts contain rules and illustrative problems related to this subject. In the present essay, an attempt is made to study these diverse types of Sanskrit sources in a combined manner and to see what light they throw on the actual state of affairs in lending money on interest. The first part deals with the nature and chronology of the administrative and legal texts and with the rules laid down in these texts on money lending, the fair rate of interest and the maximum extent to which the interest can accumulate. The second part is devoted to the rules of computation relating to loans and interest as formulated in the mathematical texts and to the examples to illustrate the rules, which are provided in the texts and in their commentaries.
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement No. 269804, Mathematical Sciences in the Ancient World.
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Notes
- 1.
Trautmann (1971).
- 2.
For a detailed study of this vast literature, see P.V. Kane’s monumental History of Dharmaśāstra which is comparable, in its expanse and in the analytical acumen, to Needham’s Science and Civilisation in China.
- 3.
Cf. the chronological table in Kane (1946: xvii–xx). Kane places the Manu-smṛti between 200 BCE and 100 CE, the Yājñavalkya-smṛti between 100 CE and 300 CE and the Nārada-smṛti between 100 CE and 400 CE.
- 4.
Manusmṛti 1.90:
paśūnāṃ rakṣaṇaṃ dānam ijyādhyayanam eva ca |
vaṇikpathaṃ kuśīdaṃ ca vaiśyasya kṛṣim eva ca ||.
- 5.
There are vague legends about certain Kṣatriya kings being experts in Vedic lore; in historical times, we come across several royal authors of learned Sanskrit texts, but there is neither legend nor historical evidence of Vaiśya scholars or authors of Sanskrit works until the second millennium CE when Sanskrit learning was cultivated especially by Vaiśyas belonging to Jainism.
- 6.
Cited in Sarma (1997: 191).
- 7.
Cited in Sarma (1997:192).
- 8.
Some medieval mnemonic tables for multiplication were collected in Sarma (1997), but nobody seems to have collected mnemonic tables of interest. However, it is not impossible to reconstruct them. The monetary unit in British India was the rupee; it was divided into sixteen annas and the anna was further subdivided into twelve pies. If the interest is 1 per cent per month, the monthly interest on 1 rupee is 192/100 pies; this has to be rounded up to 2 pies. Then the interest table with 1 per cent interest per month would run as follows:
On 1 rupee the monthly interest is 2 pies.
On 2 rupees the monthly interest is 4 pies.
…
On 6 rupees the monthly interest is 1 anna.
On 7 Rupees the monthly interest is 1 anna and 2 pies.
…
On 100 rupees the monthly interest is 1 rupee, and so on.
This would be recited in Gujarati language in a sing-song fashion. Learning such a table by heart is important, because at several instances, the interest has to be rounded up to the nearest pie.
- 9.
Though loans of other commodities such as grains or oil are occasionally mentioned, the main focus in our texts is on cash loans. On the loans of commodities other than cash; see Sect. 12.2.2.
- 10.
The only exception is the Vasiṣṭha-dharma-sūtra, one of the early texts, which, as cited in the Manu-smṛti, mentions the interest as a fraction of the principal, viz. one-eightieth part of the principal; see below.
- 11.
This mode of expression occurs in several passages to be cited below. Thus Manu-smṛti 8.140–142 employs dvikaṃ śataṃ, trikaṃ śataṃ, catuṣkaṃ śataṃ, pañcakaṃ śataṃ in the sense of ‘two per cent, three per cent, four per cent and five per cent’ respectively. In his commentary on the Brāhmasphuṭa-siddhānta, Pṛthūdaka gives an example where śatasya daśakā vṛddhiḥ occurs in the sense of ‘of/on one hundred the interest is ten’ implying thus ‘ten per cent interest’. In Līlāvatī 91, pañcakena śatena is used to mean ‘at the rate of five per cent’. Sometimes, the number word with the suffix ka is compounded with śata. Thus, in Pāṭīgaṇita 55, we find pañcaka-śatena dattaṃ rūpaśataṃ which means ‘one hundred rūpas (silver coins) were given [on loan] at five per cent [interest per month]’; likewise in Gaṇita-kaumudī, p. 73, daśaka-śatena tu dattaṃ śataṃ is used to mean ‘one hundred [coins] were given [on loan] at ten per cent [interest per month]’.
- 12.
The Arthaśāstra, to be cited below, describes the one and a quarter interest per month as dharmyā, translated by Kangle as ‘lawful’. But dharmyā can also mean ‘ethical’ or ‘just’.
- 13.
Translations of all the passages cited below from the text are by R. P. Kangle. In these and in the translations of passages from other texts to be cited below, we have added the Sanskrit technical terms in round brackets. For the sake of consistency, editorial interpolations are placed within square brackets, even when the original writer used round brackets.
- 14.
Paṇa was a copper coin weighing 20 māṣas.
- 15.
AS 3.11.1–5: sapādapaṇā dharmyā māsavṛddhiḥ paṇaśatasya. pañcapaṇā vyāvahārikī, daśapaṇā kāntāragānāṃ, viṃśatipaṇā sāmudrāṇām. …prakṣepavṛddhir udayād arthaṃ sannidhānāpannā vārṣikī deyā. It is not very clear what is meant by ‘being set apart in a store’.
- 16.
Translations of all the passages from the Manu-smṛti cited below are by Georg Bühler.
- 17.
For the sake of greater clarity, this may be rephrased as follows: in order to increase his capital, a money-lender (vārddhuṣika) may accept the interest prescribed by Vasiṣṭha, [namely] one-eightieth part in a hundred per month.
- 18.
Manu-smṛti 8.140–142:
vasiṣṭha-vihitāṃ vṛddhiṃ sṛjed vitta-vivardhinīm |
aśīti-bhāgaṃ gṛhṇīyān māsād vārddhuṣikaḥ śate ||
dvikaṃ śataṃ vā gṛhṇīta satāṃ vṛttim anusmaran |
dvikaṃ śataṃ hi gṛhṇāno na bhavaty arthakilbiṣī ||
dvikaṃ trikaṃ catuṣkaṃ ca pañcakaṃ ca samaṃ smṛtam |
māsasya vṛddhiṃ gṛhṇīyād varṇānām anupūrvaśaḥ ||.
- 19.
Yājñavalkya-smṛti 2.37:
aśītibhāgo vṛddhiḥ syān māsi māsi sabandhake |
varṇakramāc chataṃ dvi-tri-catuḥ-pañcakam anyathā ||.
- 20.
In his commentary on the Manu-smṛti 8.140–142, Kullūka Bhaṭṭa follows the Yājñavalkya-smṛti and even cites it: nanv aśītibhāgo laghu, dvikaśata-grahaṇaṃ guru, katham imau brāhmaṇasya laghu-guru-kalpau vikalpetām. atra medhātithi-govindarājau tu pūrva-vṛddhyā nirvāhāsambhave dvika-śata-parigraha iti vyācakṣāte. idaṃ tu vadāmaḥ sabandhakeṣv aśītibhāga-grahaṇaṃ bandhaka-rahite tu dvikaśata-vṛddhi-parigrahaḥ. tad āha yājñavalkyaḥ:
aśītibhāgo vṛddhiḥ syān māsi māsi sabandhake |
varṇakramāc chataṃ dvitricatuḥpañcakam anyathā ||
‘Now one-eightieth part is low, demanding two per cent is high, why then are these two lower and higher rates prescribed for the Brahmin? In this connection, Medhātithi and Govindarāja remark that the two per cent interest has been prescribed because [for the money lender] subsistence (nirvāha) was impossible at the old rate of interest [of one and a quarter per cent]. But we say that when there is a pledge or mortgage (sa-bandhaka), one-eightieth part can be accepted [as interest] and when there is no pledge two per cent should be accepted. Therefore, Yājñavalkya proclaimed, “Let the interest be one-eightieth part per month when [the loan is secured] with a pledge (sa-bandhaka); or else, two, three, four and five per cent [per month] according to the order of the castes”’.
- 21.
Translations of passages from the Nārada-smṛti cited below are by Richard Lariviere (2003).
- 22.
Nārada-smṛti 1. 86–91:
sthānalābha-nimittaṃ hi dānagrahaṇam iṣyate |
tat kusīdam iti proktaṃ tena vṛttiḥ kusīdinām ||86||
kāyikā kālikā caiva kāritā ca tathā smṛtā |
cakravṛddhiś ca śāstreṣu tasya vṛddhiḥ caturvidhā ||87||
kāyāvirodhinī śaśvat paṇapādyā tu kāyikā |
pratimāsaṃ sravati yā vṛddhiḥ sā kālikā smṛtā ||88||
vṛddhiḥ sa kāritā nāma ya ṛṇikena svayaṃkṛtā |
vṛddher api punar vṛddhiś cakravṛddhir udāhṛtā ||89||
ṛṇānāṃ sārvabhaumo ’yaṃ vidhir vṛddhikaraḥ smṛtaḥ |
deśācāravidhis tv anyo yatra-rṇam avatiṣṭhati ||90||
dviguṇaṃ triguṇaṃ caiva tathānyasmiṃś caturguṇam |
tathāṣṭaguṇam anyasmin deśe deśe ’vatiṣṭhate ||91||.
- 23.
Manu-smṛti 8.153:
nātisāṃvatsarīṃ vṛddhiṃ na cādṛṣṭāṃ punar haret |
cakravṛddhiḥ kālavṛddhiḥ kāritā kāyikā ca yā ||153||
‘Let him not take interest beyond the year (atisāṃvatsarī), nor such as is unapproved (adṛṣṭā), nor compound interest (cakra-vṛddhi), periodical interest (kāla-vṛddhi), stipulated interest (kāritā), and corporal interest (kāya)’.
- 24.
However compound interest did exist in India, at least in the nineteenth and twentieth centuries. Cf. Vesey-FitzGerald (1925: 171): ‘In nothing is this [evil of usury] more marked than in the accumulation of compound interest’.
- 25.
It implies that the interest can be less than half if the lender so agrees.
- 26.
Arthaśāstra 3.11.3: dhānyavṛddhiḥ sasyaniṣpattāv upārthaḥ, paraṃ mūlyakṛtā vardheta.
- 27.
Manu-smṛti, 8.151 cd: dhānye sade lave vāhye nātikrāmati pañcatām ||.
- 28.
Lariviere (2003: 304): ‘These amounts are in direct proportion to the possibility of adulteration of the material loaned or, in the case of clothes, the diminution of their value by use.’
- 29.
Nārada-smṛti 1–92–95:
hiraṇya-dhānya-vastrāṇāṃ vṛddhir dvi-catur-guṇā |
ghṛtasyāṣṭa-guṇā vṛddhiḥ strīpaśūnāṃ ca saṃtatiḥ ||92|
sūtra-karpāsa-kiṇvānāṃ trapuṣaḥ sīsakasya ca |
āyudhānāṃ ca sarveṣāṃ carmaṇas tāmralohayoḥ ||93|
anyeṣāṃ caiva sarveṣām iṣṭakānāṃ tathaiva ca |
akṣayyā vṛddir eteṣāṃ manur āha prajāpatiḥ ||94||
tailānāṃ caiva sarveṣāṃ madyānāṃ madhusarpiṣām |
vṛddhir aṣṭaguṇā jñeyā guḍasya lavaṇasya ca ||95||.
- 30.
There are three editions which are listed in the Bibliography. Of these, Ingo Strauch’s edition and translation into German is far superior to the others. Our English translation of the documents closely follows Ingo Strauch’s German rendering.
- 31.
Strauch, 2.32.1 (text: 170–171; translation: 372–373).
- 32.
The dramma was the basic monetary unit in several kingdoms in Central and Northern India in the twelfth, thirteenth and fourteenth centuries. The coin was made of billon, a mixture of silver and copper. Since the silver content in dramma varied in each region and in each reign, their intrinsic value also varied; cf. Sarma (2012).
- 33.
These are generally referred to as pārutthaka-drammas. The exact significance of this name is not known.
- 34.
śrī-śrīmālīya-khara-ṭaṃkaśālā+āhata-triparīkṣita-haṭṭa-vyavahāraka-pracuraṃta-śrīmat-pāraupatha. This formulaic description of the coins occurs in as many as twelve documents in the Lekhapaddhati. This must have been a standard formula in early medieval Gujarat to express the genuineness of a particular coin (cf. Sarma 2012: 9). It is not clear what khara in this expression denotes. It is possible that it refers to the kharatara-gaccha of Śvetāmbara Jains. Then the expression would mean that coins were produced at a mint maintained by the Śrīmāla Jains of the Kharatara sect or the mint maintained by the Jains of the Kharatara sect in the city of Śrīmāla. Mentioning the name of the mint is necessary because the silver content varied in dramma minted at different mints. Therefore, if the drammas minted at the Kharatara mint were given on loan, repayment had to be made in drammas from the same mint.
- 35.
In the Gujarat region, the New Year commences with the lunar month of Kārtika, corresponding to parts of October and November. Loans were repaid in this first month of the year.
- 36.
A day-and-night (ahorātra) is divided into 8 praharas (Middle Indic: pahar); the expression means the same as ‘within 24 h’.
- 37.
Strauch, 2.32.2 (text: 171–172; translation: 374).
- 38.
dvika-śata-pratyā (?) vyājaṃ caḍhati. Is this a reference to the old rule in the Manu-smṛti?
- 39.
Strauch, 2.17.5 (text: 139–140; translation: 310–313).
- 40.
Corresponds roughly to 17 April 1231 CE. It must be noted that this is not the actual date but an arbitrary one. Vīsaladeva had not yet ascended the throne at this date and the coins issued by him could not have become old.
- 41.
The festival is commonly known as Dīpāvalī or Diwali; it occurs on the last day of the lunar month of Āśvina, in October or November in the modern calendar.
- 42.
Arthaśāstra 3.11.6: cirapravāsaḥ saṃsthambha-praviṣṭo vā mūlya-dviguṇaṃ dadyāt.
- 43.
Gautama-dharma-sūtra, 12.31: cirasthāne dvaiguṇyaṃ prayogasya. The translation cited above is by Georg Bühler (1879).
- 44.
Manu-smṛti, 8.151ab: kusīdavṛddhir dvaiguṇyaṃ nātyeti sakṛd āhitā (v.l. sakṛd āhṛtā) |.
- 45.
Kullūka (ibid.): vṛddhyā dhanaprayogaḥ kusīdaṃ tatra yā vṛddhiḥ sā dvaiguṇyaṃ nātikrāmati mūlavṛddhir dviguṇaiva bhavati. pratidina-pratimāsādi-grāhyaiti tātparyam.
- 46.
Translations of all passages from Medhātithi’s commentary are by Ganganath Jha (1999).
- 47.
Medhātithi II: 142: naivam. guṇo ’vayava ucyate. sa tāvad avayavinam apekṣate. prakṛtaṃ ca dhanam. ataḥ prayogaviṣayasya dhanasyānena prakāreṇa dvaiguṇyam uktaṃ bhavati. The translation is by Ganganath Jha (ibid., VI: 186–87).
- 48.
Ibid., II: 144: ye tu vyācakṣate, yā vṛddhir upacitā sāṃvatsarī yugapat sarvaivānīyate tatrāyaṃ vidhiḥ, yā punaḥ prāptadhanāpi sarvā na dīyate tatra dviguṇād adhikam api. teṣāṃ na na-śabdo yathārtho nāpi āhita iti. sāṃvatsarī tāvad upacitā grāhyā dvitīyasaṃvatsare punar ānayanam asyeti na kvacid dvaiguṇya-niyamaḥ syāt. The translation is by Ganganath Jha (ibid., VI: 190).
- 49.
Ibid., II: 143: sakṛd āhitā. sakṛd ity anena vyavasthāpito ’ṅgīkṛtaḥ punaḥ punaḥ prayoga iti yāvat. ādhānam sthāpanam ucyate. vacana-vyavasthā ca nirūpaṇaṃ sthāpanam eva. punaḥ prayogaś ca dviguṇībhūte dhane ādīyamāne bhavati. yadā dviguṇo hi vṛddhyartha uttamarṇo ’dhamarṇaś ca tadīyena dhanena mahat kāryaṃ kariṣyan karaṇaparivṛttiṃ karotīti yā praktanī vṛddhir iyaṃ vādyaprabhṛti vardhata iti. tadā dviguṇabhūtam api punar vardhata eva. The translation is by Ganganath Jha (ibid., VI: 189).
- 50.
Vesey-FitzGerald (1925: 172).
- 51.
Ibid., 172, note 2.
- 52.
Ibid.
- 53.
Ibid., 177.
- 54.
Kane (1946: 422–425).
- 55.
Kane (1946: 425).
- 56.
Jois (1984: 88–89).
- 57.
- 58.
For a translation and study of Bhāskara I’s commentary on the mathematical chapter of the Āryabhaṭīya cf. Keller (2006).
- 59.
The commentary has not been published. Some of his examples are cited by Sudhākara Dvivedī in his edition of the Brāhmasphuṭa-siddhānta. Colebrooke (1817) translated some examples into English in his notes.
- 60.
This and the next section are substantially based on Sarma (2002), which may be consulted for detailed references.
- 61.
Āryabhaṭīya 2. 26–27ab:
trairāśikaphalarāśiṃ tam athecchārāśinā hataṃ kṛtvā |
labdhaṃ pramāṇabhajitaṃ tasmād icchāphalam idaṃ syāt | |
chedāḥ parasparahatāḥ bhavanti guṇakāra-bhāgahārāṇām |.
- 62.
Bhāskara I, 120:
śatavṛdḥir māse syāt pañca kiyan māsaṣaṭprayuktāyāḥ |
vṛddḥiṃ vada viṃśatyā yadi bhaṭagaṇitaṃ tvayā buddham | |.
- 63.
The first Rule of Three is as follows: if on 100, the interest per month is 5, what is the interest on 20? The three given terms are placed in the order 100, 5, 20; the term (icchā) is multiplied by the middle term (phala) and divided by the first term (pramāṇa). The result is 1.
- 64.
Ibid.: karaṇam-prathama-trairāśikaṃ 100, 5, 20. labdhaṃ rūpakaḥ 1. dvitīya-trairāśikaṃ yadi māsena rūpakaḥ ṣaḍbhiḥ kiyanta iti labdhaṃ rūpakaḥ ṣaṭ.
- 65.
Ibid.: etad eva gaṇitaṃ yugapat kriyamāṇaṃ pañcarāśikaṃ bhavati. tatrāpi śatasya māse iti pramāṇa-dvayam, pañceti phala-rāśiḥ viṃśatyā ṣaḍbhir māsaiḥ kim iti viṃśatiḥ ṣaṭ ca icchā-rāśiḥ. tatra pūrvavad eva icchā-rāśiḥ phala-rāśinā guṇitaḥ pramāṇa-rāśibhyāṃ vibhajyate phalaṃ pūrvavad eva. trairāśikam evaitad dvidhā vyavasthitam. chedā api pūrvavad guṇakāra-bhāgahārāṇāṃ parasparaṃ gacchanti.
- 66.
Ibid.: 121:
viṃśatyāḥ sārdhāyāḥ satryaṃśaḥ rūpakao bhaved vṛddhiḥ |
māse sapañcabhāge pādonānāṃ tu saptānām ||
māsaiḥ ṣaḍbhiḥ vācyaṃ daśabhāgayutais tu kā bhaved vṛddhiḥ |
jñātvā cheda-vikalpaṃ samyak bhaṭatantrasūtreṇa ||.
- 67.
Bhāskara I states the result in silver coins thus: labdhaṃ rūpakadvayaṃ 2, viṃśopakāḥ 4, viṃśopakabhāgāś ca 26/41, ‘the quotient is 2 rūpakas, 4 viṃśopakas and 26/41th part of a viṃśopaka’. The rūpaka was a silver coin, used as standard currency in many periods and in many parts of India, and the viṃśopaka was its twentieth part.
- 68.
Ganeśa Daivajña, Buddhivilāsinī, p. 76: pramāṇa-sambandhi-rāśayas tatphalaṃ caikasmin pakṣe ’dho ’dhaḥ sthāpyam. icchā-sambandhi-rāśayo ’nyapakṣe samāna-jātitvam atrāpy anuvartate. ‘Quantities related to the argument should be arranged on one side one below the other. Quantities related to the requisition [should be similarly arranged] on another side. Here also the rule of belonging to the same denomination (samāna-jātitva) applies’.
- 69.
In Sanskrit manuscripts, the denominators and the nominators of fractions are written one below the other without separating them with a horizontal line. Again, in some manuscripts, a zero is written in the cell for the unknown quantity (jñeya), just as we write an x today. This can be seen in the examples from Pṛthūdaka’s commentary to be discussed below. This zero is a mere symbol and should not be confused with the quantity zero, nor used in the multiplication along with the other numbers in the column.
- 70.
Brāhmasphuṭa-siddhānta 12.11–12:
trairaśikādiṣu phalaṃ viṣameṣv ekādaśānteṣu |
phalasaṅkramaṇam ubhayato bahurāśivadho ’lpavadhahṛto jñeyam |
sakaleṣv evaṃ bhinneṣūbhayataś chedasaṅkramaṇam | |
Usually, there is only one fruit, which pertains to the argument side. But Brahmagupta mentions two fruits here because there can also be problems where the fruits or the interests of two sides are given and one is asked to compute the principal or the time on the requisition side. Such examples are given below. See, e.g., the third example given by Pṛthūdaka to be cited soon.
- 71.
Brāhmasphuṭa-siddhānta, Dvivedī’s edition (1902: 180):
śatasya daśakā vṛddhis tribhir māsair nirūpitā |
pañcamāsaprayuktāyāḥ ṣaṣṭer labho nigadyatām ||
The translation cited above is by Colebrooke (1817: 284).
- 72.
Ibid.:
māsena satribhāgena sārdhāyās triṃśateḥ phalam |
adhyardhaṃ yadi varṣeṇa sārdhaṣaṣṭer ihocyatām ||
The translation cited above is by Colebrooke (1817: 284).
- 73.
Ibid.:
śatasya daśabhir māsaiś catvāriṃśat phalaṃ yadi |
māsāṣṭake śataṃ labdhaṃ kasyeyaṃ vṛdḥir ucyatām ||
The translation cited above is by Colebrooke (1817).
- 74.
Brāhmasphuṭa-siddhānta 12.14ab = Gaṇita-tilaka (p. 85, line 19):
kālaguṇitaṃ pramāṇaṃ phalabhaktaṃ vyekaguṇahataṃ kālaḥ |
- 75.
Brāhmasphuṭa-siddhānta, Dvivedī’s edition (1902: 182):
śatadvayasya māsena ṣad drammā yadi vṛdḥitaḥ |
triguṇaṃ kena kālena prayuktaṃ tad dhanaṃ bhavet ||
The translation is by Colebrooke (1817: 287). The same example occurs also at Gaṇita-tilaka 125.
- 76.
The translation is by Shukla (1959: 35).
- 77.
Pāṭī-gaṇita, Rule 47:
nijakālenāhanyāt pramaṇarāśiṃ phalena parakālam |
tau svayutihṛtau syātāṃ miśraguṇau mūlavṛddhidhane ||
- 78.
Āryabhaṭīya 2.25:
mūlaphalaṃ saphalaṃ kālamūlaguṇam ardhamūlakṛtiyuktam |
tanmūlaṃ mūlārdhonaṃ kālahṛtaṃ svamūlaphalam ||
- 79.
Shukla (1976: 68).
- 80.
Bhāskara I, 114:
jānāmi śatasya phalaṃ na ca kintu śatasya yat phalaṃ saphalam |
māsaiś caturbhir āptaṃ ṣad vada vṛddhiṃ śatasya māsottham ||
- 81.
Brāhmasphuṭa-siddhānta 12.15:
kāla-pramāṇa-ghātaḥ para-kāla-hṛto dvidhādyamiśra-vadhāt |
anyārdhakṛtiyutāt padam anyārdhonaṃ pramāṇa-phalam ||
Cf. Gaṇita-sāra-saṅgraha 6.44.
- 82.
Brāhmasphuṭa-siddhānta, Dvivedī’s edition (1902: 183):
ajñātavṛddhikarṇatvaṃ drammāṇāṃ śatapañcakam |
vṛddhir māsacatuṣkasya tadīyānyatra yojitā ||
kalāntareṇa tenaiva jātāṣṭāsaptatis tataḥ |
masair daśabhir atra tvaṃ pramāṇasya phalaṃ vada ||
The Dvivedī edition reads the first word in the third line as kālāntareṇa. Our emendation is based on the manuscript Eggeling 2769. The translation cited above is by Colebrooke (1817: 288).
- 83.
Līlāvatī 90:
pramāṇa-kālena hataṃ pramāṇaṃ vimiśra-kālena hataṃ phalaṃ ca |
svayogabhakte ca pṛthaksthite te miśrāhate mūla-kalāntare staḥ |
yad veṣṭakarmākhyavidhes tu mūlaṃ miśrāc cyutaṃ tac ca kalāntaraṃ syāt | |
- 84.
Cf. Pāṭī-gaṇita, Rule 47; Brāhmasphuṭa-siddhānta 12.14 cd (the rule only for p).
- 85.
Līlāvatī 91:
pañcakena śatenābde mūlaṃ svaṃ sakalāntaram |
sahasraṃ cet pṛthak tatra vada mūlakalāntare ||
- 86.
Līlāvatī 92:
atha pramāṇair guṇitāḥ svakālā vyatīta-kāla-ghna-phalodḥṛtās te |
svayoga-bhaktāś ca vimiśra-nighnāḥ prayukta-khaṇḍāni pṛthag bhavanti ||
- 87.
According to Līlāvatī 2, a niṣka is a coin equal in value to 16 drammas.
- 88.
Līlāvatī 93:
yat pañcaka-trika-catuṣka-śatena dattaṃ khaṇḍais tribhir gaṇaka niṣka-śataṃ ṣaḍūnam | māseṣu sapta-daśa-pañcasu tulyam āptaṃ khaṇḍatraye ’pi hi phalaṃ vada khaṇḍasaṃkhyam ||
- 89.
Līlāvatī 94:
prakṣepakā miśra-hatā vibhaktāḥ prakṣepayogena pṛthak phalāni |
- 90.
Cf. Brāhmasphuṭa-siddhānta 12.16ab, Pāṭī-gaṇita 59(i).
- 91.
Līlāvatī 95:
pañcāśad ekasahitā gaṇakāṣṭaṣaṣṭiḥ pañconitā navatir ādidhanāni yeṣām |
prāptā vimiśritadhanais triśatī tribhis tair vāṇijyate vada vibhajya dhanāni teṣām ||
- 92.
Pāṭī-gaṇita, Rule 49–50:
īpsita kālopanaye mūlaṃ mūlāt pṛthak pṛthag jahyāt |
śeṣasya māsikaphalaṃ viśodhayen māsikopanayāt| |49 | |
śeṣeṇa māsikaphalaṃ māsaguṇaṃ māsaśeṣayug vibhajet |
labdhaṃ gatamāsa-yutaṃ dhana-praveśe bhavet kālaḥ | |50 | |
The translation cited above is by Shukla (1959: 32–33). In the note on his English translation, Shukla mentions that the reading māsaśeṣayug in 50b should be mūlaśeṣayug. If this is so, this reading is also the same as that in the Gaṇita-kaumudī of Nārāyaṇa.
- 93.
Pāṭī-gaṇita, Examples 55–56:
pañcaka-śatena dattaṃ rūpa-śataṃ yasya kasyacid dhaninā |
gṛham ādattaṃ tasmāt prati-māsaṃ dviguṇa-viṃśatyā | |55 | |
ṛṇamuktas tatkiyatā kālena sa bhaved ṛṇī samācakṣva |
dhaninaḥ praviśati vidvan kiṃ śuddhasthānalābhena | |56 | |
- 94.
We have underlined the common expressions in the two rules; the few words that are different in the Gaṇita-kaumudī are just the synonyms of the words in the Pāṭī-gaṇita. In his introduction to the edition of Pāṭī-gaṇita, Shukla (1959: xvi–xvii) refers to the rule and the example, and states: ‘This rule and example, too, do not occur in any work written before the tenth century A.D. and seem to be due to Śrīdharācārya. The occurrence of this rule and a similar example in the Gaṇita-kaumudī of Nārāyaṇa proves Śrīdhara’s influence on Nārāyaṇa’.
- 95.
Gaṇita-kaumudī, pp. 72–73:
skandhaka-kālopanayān mūlaṃ mūlāt pṛthak pṛthak tyaktvā |
avaśiṣṭasya ca māsikaphalaṃ tyajen māsikopanayāt ||
śeṣeṇa māsikaphalaṃ māsaghnaṃ mūlaśeṣayug vibhajet |
labdhaṃ gatamāsa-yutaṃ dhanasyanirmuktakālaḥ syāt ||
- 96.
Gaṇita-kaumudī, p. 73:
daśakaśatena tu dattaṃ śataṃ ca pañcāśad uttaraṃ dhaninā |
pratimāsam ṛṇī saphalaṃ pañcāśat skandhakaṃ prayacchati ca |
anṛṇī kālena sakhe prajāyate kena kathayāśu |
- 97.
From the next sentence onwards, Nārāyaṇa uses the term skandha-dhana in the sense of the amount of the monthly instalment, which in the present example is 50, and designates the amount of money being returned in each instalment (i.e. 50—interest) as mūla. Therefore, we shall render henceforth skandha-dhana as the ‘monthly instalment’ and mūla as ‘basic amount’.
- 98.
The printed text reads 2075/43 which is a misprint.
- 99.
The printed text has pūrvamūlam etac cheṣād apāsya; but it should read mūlam etat pūrva-śeṣād apāsya.
- 100.
See footnote 10 above; see also the final example cited above in Sect. 12.2.2 from the Gaṇita-kaumudī, where the rate of interest is as high as 10%.
- 101.
This is also the first title of law in the Nārada-smṛti. Lariviere (2003: 273) renders it as ‘Non-payment of debts’, splitting the compound as ṛṇa-adāna, and not correctly as ṛṇa-ādāna. Surely Nārada does not aim to teach how not to repay debts!
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Appendix 12: Technical Terms
Appendix 12: Technical Terms
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Money-lending: kusīda, prayoga
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Money-lender/creditor: uttamarṇa, kusīdin, dhanika, dhanin, prayojaka, vārddhuṣika
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Debtor/borrower: adhamarṇa, ṛṇika, ṛṇin, dhāraṇika
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Loan/debt: ṛṇa, uddhāra
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Principal: mūla
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Capital: dhana
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Interest: kalāntara, phala, vṛddhi, vyāja, vyājaka,
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Repayment of loan: ṛṇādānaFootnote 101
It may be noted that the technical terms dhana and ṛṇa, used in mathematical texts in the sense of ‘positive’ and ‘negative’ number respectively, are derived from the terminology of money-lending.
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Sarma, S.R., Kusuba, T. (2020). Loans and Interest in Sanskrit Legal and Mathematical Texts. In: Michel, C., Chemla, K. (eds) Mathematics, Administrative and Economic Activities in Ancient Worlds. Why the Sciences of the Ancient World Matter, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48389-0_12
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