As per given question,
Face Value F = 450,
True discount = 90
As we know the formula,
Present Worth, PW = Face Value ? True Discount
Present Worth, PW = F ? TD = 540 ? 90 = Rs. 450
Hence Simple Interest on 450 = 90 ? ? ? ? ? ? ? ? ? ? ( 1 )
Simple Interest on the face value = Bankers Discount
? Simple Interest on 540
Hence, Simple Interest on 540 = 90/450 × 540 = Rs. 108 = Bankers Discount
T.D. = ?P.W. x B.G.
or B.G. = (T.D.)2/P.W. = (110 X 110) / 1100 = Rs. 11
? B.D. = B.G. + T.D. = Rs. (11 + 110) = Rs. 121
Let TD = N, then BD = 11N/10
Sum = (BD x TD) / (BD - TD) = [(11N/10) x N] / [11N/10 - N]
= [11N2/10] / [N/10] = 11N
SI on ? 11N for 4 yr is ? 11N/10.
? Rate = (100 x 11N/10)/(11N x 4)% per annum
= 2.5% per annum
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