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## BANKERS DISCOUNT -> IMPORTANT CONCEPTS

 Bankers’ Discount : Suppose a merchant A buys googds worth, say Rs. 10,000 from another merchant B at a credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months. The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it to get a date, known as legally due date. Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I. on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is known as Banker’s Dicount (B.D.) Thus, B.D. is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date. Banker’s Gain (B.G.) = (B.D.) - (T.D.) for the unexpired time. Note : When the date of the bill is not given, grace days are not to be added.

## BANKERS DISCOUNT -> IMPORTANT FORMULAE

 I. B.D. = S.I. on bill for unexpired time. II. B.G. = (B.D.) - (T.D.) = S.I. on T.D. = (T.D.)² / R.W. III. T.D. = √P.W. * B.G. IV. B.D. = [Amount * Rate * Time / 100] V. T.D. = [Amount * Rate * Time / 100 + (Rate * Time)] VI. Amount = [B.D. * T.D. / B.D. - T.D.] VII. T.D. = [B.G. * 100 / Rate * Time]

## BANKER’S DISCOUNT -> SOLVED EXAMPLES

1. What rate percent does a man get for his money when is discounting a bill due 10 months hence, he deducts 10% of the amount of the bill Sol.Let, amount of the bill = Rs. 100. Money deducted = Rs.10. Money received by the holder of the bill = Rs. (100 - 10) = Rs. 90. ∴ S.I. on Rs. 90 for 10 months = Rs. 10. ∴ Rate = [100 * 10 / (90 * 10/12)] % = 13⅓%. The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker’s discount is: T.D. = [B.G. * 100 / R * T] = Rs. [270 * 100 / 12 * 3] = Rs. 750. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent. Sol.Sum = [B.D. * T.D. / B.D. - T.D.] = Rs. [120 * 110 / 120 - 110] = Rs. 1320. Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120. ∴ Rate = [100 * 120 / (1320 * 2/3)]% = 13 7/11%

## BANKER’S DISCOUNT -> EXERCISE

1. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?

• A. 100
• B. 115
• C. 120
• D. 129
 Ans: D. Sol. 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.

2. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the banker’s gain.

• A. 120
• B. 121
• C. 130
• D. 151
 Ans: B. Sol. T.D. = √P.W. * B.G. ∴ B.G. = (T.D.)² / T.W. = Rs. [110 * 110 / 1100] = Rs. 11. ∴ B.D. = (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.

3. The banker’s discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:

• A. 210
• B. 280
• C. 360
• D. 450
 Ans: C. Sol. Sum = B.D. * T.D. / B.D. - T.D. = Rs.[72 * 60 / 72 - 60] = Rs. [72 * 60 / 12] = Rs. 360.

4. The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :

• A. 2 months
• B. 4 months
• C. 6 months
• D. 7 months
 Ans: B. Sol. S.I. on Rs. 1600 = R.D. on Rs. 1680. ∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 15%. ∴ Time = [100 * 80 / 1600 * 15] year = 1/3 year = 4 months.

5. The present wort of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is :

• A. 36
• B. 52
• C. 66
• D. 96
 Ans: D. Sol. T.D. = √P.W. * B.G. = √576 * 16 = 96.