________________
108.
GANITASĀRASANGRABA.
optionally chosen (maximum available amount of an instalment) hy (whatever happens to he) the outstanding (fractional part of the number of terms in the scrics), to the amount of the (first) instalment as multiplicd by the sum of that series in arithmetioal progression, which has (one for the first term, one for the common difference, and has for the number of torms the integral value of) the quotient obtained by dividing the above optionally chosen maximum) amount of debt (dischargod at an instalment) by the (above amount of the first) instalment. The interest thereon is that which accrues for the period of an instalmont. The time (of an instalment) divided by the amount of the first) instalment and multiplied by the (optionally chosen maximum) amount of debt (discharged at an instalment) gives rise to the time (which is the time of the discharge of the whole dobt).
Examples in illustration thereof. 72 and 731. A certain man ntilised, (for the discharge of a debt) bearing interest at 5 por cent (per month), 60 (as the available maximum amount) with 7 as the first instalment amount, increasing it by 7 in Bucoceive instalments due every of a month. ile thus gavo in discharge of the debt the sum of a series in arithmetical progrossion consisting of forms, and gave also the interest accruing on those multiples of 7. What is the debt anivunt corresponding to the sum of the series, whut is that interont (which he paid), and (what is the time of discharge of that debt ?
734 to 76. A certain man utilised for the discharge of u delt, bearing interest at 5 per cent (per munscm), 80 (as the available maximum amount) with 8 as the first instalment amount, increasing it by 8 in successivo instalments due every of a month. He thus
8 ropresents the number of terus of the series in arithimetical progression. which has 1 for the first term und 1 for the common difference; and in the agru or the outstanding fractional part. The sum of the above-mentioneel serios, viz., 30, multiplied by 7, the amount of the first instalment, is added to the product of und 60, which latter is the maximum available amount of an Instalment. Thus, we get 36 X 7+;X 60 = 4, which is the required capital amount in the due debt. The interest on 844 fort of a month at the rate of 5 per cent per mengem will be the interest paid on the whole. The time of discharge will be ( 7) X 20 = 4 months.
