# Banker's Discount

The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270.The banker’s discount is :

⇒ TD = $$\frac{BG \times 100}{R \times T}$$

= Rs. $$\frac{270 \times 100}{12 \times 3}$$

= Rs. 750

∴ B.D. = Rs. (750 + 270) = Rs. 1020.

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

⇒ TD = $$\sqrt{PW \times BG}$$

= $$\sqrt{576 \times 16}$$

= 96

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 :

S.I. on Rs. 1600 = T.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 = $$\left ( \frac{100 \times 80}{1600 \times 15} \right )$$ year

= $$\frac{1}{3}$$ year

= 4 months

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 :

Sum = $$\frac{BD \times TD}{BD - TD}$$

= Rs. $$\frac{72 \times 60}{72 - 60}$$

= Rs. $$\frac{72 \times 60}{12}$$ = Rs. 360

The true discount on a bill of Rs. 540 is Rs. 90. The Banker’s discount is :

P.W. = Rs. (540 − 90) = Rs. 450.

∴    S.I on Rs. 450 = Rs. 90

S.I on Rs. 540 = Rs.  $$\left ( \frac{90}{450} \times 540 \right )$$ = Rs. 108.

∴   B.D. = Rs. 108

The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker’s discount is :

BG = \frac{TD^{2}}{PW} = Rs. \frac{36 \times 36}{800} = Rs. 1.62

∴ BD = (TD + BG)
= Rs. (36 + 1.62)
= Rs. 37.62

The present worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker’s gain is :

$$BG = \frac{TD^{2}}{PW}$$

= Rs. $$\frac{160 \times 160}{1600}$$

= Rs. 16

The banker’s gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. the present worth is :

$$TD = \left ( \frac{BG \times 100}{Rate \times Time} \right )$$

= Rs. $$\left ( \frac{100 \times 120}{10 \times 2} \right )$$

= Rs. 120

$$PW = \frac{100 \times TD}{Rate \times Time}$$

= Rs. $$\left ( \frac{100 \times 120}{10 \times 2} \right )$$

= Rs. 600

The banker’s discount on a bill due 4 months hence at 15% is Rs. 420.The true discount is :

$$TD = \frac{BD \times 100}{100 + \left ( R \times T \right )}$$

= Rs. $$\left [ \frac{420 \times 100}{100 + \left ( 15 \times \frac{1}{3} \right )} \right ]$$

= Rs. $$\frac{420 \times 100}{105}$$

= Rs. 400

The banker’s gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is :

$$TD = \frac{BG \times 100}{R \times T}$$
= Rs. $$\left ( \frac{6 \times 100}{12 \times 1} \right )$$