Banker's Discount
- The banker’s gain on a certain sum due 2.5 years hence is 9/25 times of the banker’s discount. What is the rate percent?
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Let the banker’s discount, BD = Rs. 1
Then, banker’s gain, BG = 9 × 1 = Rs. 9 25 25
BG = BD − TD⇒ 9 = 1 − TD 25 ⇒ TD = 1 − 9 = 16 25 25 F = BD × TD BD − TD = 1 × 16 25 1 − 16 25
Correct Option: D
Let the banker’s discount, BD = Rs. 1
Then, banker’s gain, BG = 9 × 1 = Rs. 9 25 25
BG = BD − TD⇒ 9 = 1 − TD 25 ⇒ TD = 1 − 9 = 16 25 25 F = BD × TD BD − TD = 1 × 16 25 1 − 16 25 = 16 25 9 25 = Rs. 16 9
BD = Simple Interest on the face value of the bill for unexpired time= FTR 100 ⇒ 1 = 16 x 5 x R 9 2 100 ⇒ R = 100 × 9 = 22 1 % 40 2
- The banker’s gain of a certain sum due 3 years hence at 10 % per annum is Rs. 36. What is the present worth (PW)?
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As per given question,
Present worth PW = ?
Banker gain = 36
Time = 3 years
Rate of interest R = 10 %
True Discount = ?
As we know the formula,True Discount = Banker's Gain × 100 Time x Rate of interest ⇒ TD = 36 × 100 = Rs. 120 3 × 10
Apply the below formula to calculate the Present worth (PW)True Discount = Present Worth × Time x Rate of Interest 100
Correct Option: A
As per given question,
Present worth PW = ?
Banker gain = 36
Time = 3 years
Rate of interest R = 10 %
True Discount = ?
As we know the formula,True Discount = Banker's Gain × 100 Time x Rate of interest ⇒ TD = 36 × 100 = Rs. 120 3 × 10
Apply the below formula to calculate the Present worth (PW)True Discount = Present Worth × Time x Rate of Interest 100 ⇒ 120 = Present Worth × 3 × 10 ⇒ Present Worth = Rs. 400 100
- The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker’s discount?
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As per given question,
Present worth PW = 1296
Banker gain = ?
True Discount = 72
As we know the formula,Banker's Gain = (True Discount)2 Presence Worth
Correct Option: A
As per given question,
Present worth PW = 1296
Banker gain = ?
True Discount = 72
As we know the formula,Banker's Gain = (True Discount)2 Presence Worth ⇒ Banker's Gain = 72 x 72 = Rs. 4 1296
Apply the below formula to calculate the Banker's Discount
Banker's discount = True Discount + Banker's gain
⇒ BD = TD + BG
⇒ BD = 72 + 4 = Rs. 76
- What is the banker’s discount if the true discount on a bill of Rs. 540 is Rs. 90?
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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 )Correct Option: A
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
- The banker’s discount on a certain amount due 2 years hence is 11/10 of the true discount. What is the rate percent?
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Let us assume that the True Discount = D
As per given question,
Banker’s discount = D x 11/10 = 11D/10
Time T = 2 Years
Rate of Interest R = ?
As we know the formula,Banker's Discount = Face value x Time x Rate of interest 100 BD = F x T x R 100
Use the formula to get the face value, As we know that,Face Value F = Banker's Discount x True Discount Banker's Discount – True Discount ⇒ F = BD x TD BD – TD ⇒ F = D x 11D/10 (11D/10) – D ⇒ F = D x 11D/10 (11D - 10D)/10 ⇒ F = D x 11D/10 D/10 ⇒ F = D x 11 1
⇒ F = 11D
As we know that from above formula,BD = F x T x R 100
Correct Option: B
Let us assume that the True Discount = D
As per given question,
Banker’s discount = D x 11/10 = 11D/10
Time T = 2 Years
Rate of Interest R = ?
As we know the formula,Banker's Discount = Face value x Time x Rate of interest 100 BD = F x T x R 100
Use the formula to get the face value, As we know that,Face Value F = Banker's Discount x True Discount Banker's Discount – True Discount ⇒ F = BD x TD BD – TD ⇒ F = D x 11D/10 (11D/10) – D ⇒ F = D x 11D/10 (11D - 10D)/10 ⇒ F = D x 11D/10 D/10 ⇒ F = D x 11 1
⇒ F = 11D
As we know that from above formula,BD = F x T x R 100 ⇒ 11D/10 = 11D × 2 × R 100 ⇒ 1 = 1 × 2 x R 10 ⇒ R = 10 2
⇒ R = 5%
