पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

DETERMINATIONS 31
DETERMINATIONS (Vyavahāra)
(1) Determinations pertaining to mixtures of things
(miśraka-vyavahāra)
(i) SIMPLE INTEREST
Rule for finding the capital and the interest, when the
amount and the rate of interest are given :
47. Multiply the argument (pramāṇa-rāśi) by its time,
and the other time by the fruit (phala) ; divide each of those
(products) by their sum, and multiply by the amount (i.e.,
capital plus interest). The results (thus obtained) give the
capital (mūla-dhana) and the interest (vṛddhi-dhana) respectively.¹
That is,
argument × time × amount
Capital = ──────────────────────────────────────────────
argument × time + fruit × other time
fruit × other time × amount
Interest = ────────────────────────────────────────────── ·
argument × time + fruit × other time
Ex. 52. The rate of interest being 5 per cent per
month, a certain sum is seen to amount to 96 in a year. Say,
friend, what is the capital and what the interest ?²
Here argument = 100, time = 1 month, fruit = 5, amount = 96,
and other time = 1 year, i.e., 12 months. Therefore
100 × 1 × 96
Capital = ──────────────────── = 60,
100 × 1 + 5 × 12
5 × 12 × 96
Interest = ──────────────────── = 36.
100 × 1 + 5 × 12
Ex. 53. The interest on 100½ for one month and a
quarter being 1½, a certain sum amounts to 36½ in a period
of 7½ months. (Find the sum and the interest accrued
thereon).
Rule for separating the capital, interest, and the commission
of the surety etc., from the given amount :
48. Divide the product of the argument and its time
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¹ Cf MSi, xv. 31; GT, p. 82, vs. 111 ; SiŚe, xiii. 17; L (ASS), p. 85,
vs. 90. Also see BrSpSi, xii. 14 (ii); GSS, vi. 21, 23.
² The same example occurs in GT, p. 83, vs. 112. Also see GSS,
vi. 22, 24; L (ASS), p. 86, vs. 91; GK, I, p. 60, lines 10-11. Similar
examples occur also in Pṛthūdaka's comm. on BrSpSi, xii. 14.
Indological Truths