B.G = S.I On T.D
= Rs. (120 * 15 * 1/2 * 1/100)
= Rs.9
B.D - T.D = Rs.9
B.D = Rs.(120 +9) = Rs.129
B.G. =(T.D.)^2/P.W.
= Rs. (160*160)/1600 = Rs. 16.
T.D. =Ö(P.W.*B.G)
B.G. =(T.D.)2/ P.W.
= Rs.[(110x110)/ 1100]
= Rs. 11.
B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
F = Rs. 498
TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5%
=> T = 3/4 years = 9 months
Sum = (B.D * T.D) / (B.D) -(T.D)
= (120 * 110) / (120 -110)
= 1320
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.
Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.
F = Rs. 2160
TD = Rs. 360
PW = F - TD = 2160 - 360 = Rs. 1800
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=(360/1800)* 2160
= (1/5) * 2160
=Rs. 432
T= 6 months = 1/2 year
R = 6%
F = Rs. 8100
R = 5%
T = 3 months = 1/4 years
Therefore BD - TD = 101.25-100 = Rs.1.25
Sum =(B.D. x T.D.)/(B.D. - T.D.)
= Rs. (72 x 60) / (72 - 60)
= Rs. (72 x 60) /12
= Rs. 360.
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