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
- A bill is discounted at 10 % per annum. If banker’s discount is allowed, at what rate % should the proceeds be invested so that nothing will be lost?
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Let the amount = Rs. 100 Then BD = Rs. 10 ( ∵ banker’s discount, BD is the simple Interest on the face value of the bill for unexpired time and bill, in this case, is discounted at 10% per annum)
Proceeds = Rs. 100 − Rs. 10 = Rs. 90
Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost.
As we know the Simple interest formula,⇒ Simple interest = Principal × Time × Rate of Interest 100
As per given question,
Simple interest = 10,
Principle amount = 90
Time = 1 year
Rate of interest = RCorrect Option: B
Let the amount = Rs. 100 Then BD = Rs. 10 ( ∵ banker’s discount, BD is the simple Interest on the face value of the bill for unexpired time and bill, in this case, is discounted at 10% per annum)
Proceeds = Rs. 100 − Rs. 10 = Rs. 90
Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost.
As we know the Simple interest formula,⇒ Simple interest = Principal × Time × Rate of Interest 100
As per given question,
Simple interest = 10,
Principle amount = 90
Time = 1 year
Rate of interest = R⇒ 10 = 90 × 1 × R 100 ⇒ R = 11 1 % 9
- A banker paid Rs. 5767.20 for a bill of Rs. 5840, drawn of April 4 at 6 months. If the rate of interest was 7 %, what was the day on which the bill was discounted?
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As per given question,
Face Value F = 5840
Banker discount BD = Face Value - Paid by banker = 5840 - 5767.20 = 72.8
Rate of interest = 7 %
As we know the formula,BD = F x T x R 100 ⇒ 72.8 = 5840 × T × 7 100
Correct Option: D
As per given question,
Face Value F = 5840
Banker discount BD = Face Value - Paid by banker = 5840 - 5767.20 = 72.8
Rate of interest = 7 %
As we know the formula,BD = F x T x R 100 ⇒ 72.8 = 5840 × T × 7 100 ⇒ T = 13 × 365 days = 65 days 73
⇒ Unexpired Time = 65 days
⇒ Given that Date of Draw of the bill = 4th April at 6 months ⇒ 4th October
⇒ Legally Due Date = (4th October + 3 days) = 7th October
Hence, The date on which the bill was discounted
= (7th October − 65 days) = 3rd August
- Shankara buys a watch for Rs. 1,950 in cash and sells it for Rs. 2,200 at a credit of 1 year. If the rate of interest is 10% per annum, he _____ :
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As per given question,
Amount A = 2200
Rate of Interest R = 10 %
Time = 1 year
S.P. = P.W. of Rs. 2200 due 1 year hencePrinciple Amount = Rs. A x 100 100 + ( R x T )
Correct Option: B
As per given question,
Amount A = 2200
Rate of Interest R = 10 %
Time = 1 year
S.P. = P.W. of Rs. 2200 due 1 year hencePrinciple Amount = Rs. A x 100 100 + ( R x T ) Principle Amount = Rs. 2200 x 100 100 + ( 10 x 1 ) Principle Amount = Rs. 2200 x 100 110
Principle Amount = Rs. 20 x 100 = Rs. 2000
∴ Gain = Rs. (2000 − 1950) = Rs. 50.
- A bill for Rs. 3000 is drawn on 14th July at 5 months. It is discounted on 5th October at 10 %. What is the Banker’s Discount BD?
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As per the given all information in above question , we have
Date on which the bill is drawn = 14th July at 5 months i.e., Nominally Due Date = 14th December
Legally Due Date = 14th December + 3 days = 17th December
Date on which the bill is discounted = 5th October⇒ Unexpired Time = 73 Days = 1 year 5
Banker's Discount = Simple Interest on the face value of the bill for unexpired timeBanker's Discount = FTR 100
Here , F = 3000 , T = 1 / 5 year , Rate = 10%Correct Option: A
As per the given all information in above question , we have
Date on which the bill is drawn = 14th July at 5 months i.e., Nominally Due Date = 14th December
Legally Due Date = 14th December + 3 days = 17th December
Date on which the bill is discounted = 5th October⇒ Unexpired Time = 73 Days = 1 year 5
Banker's Discount = Simple Interest on the face value of the bill for unexpired time
Here , F = 3000 , T = 1 / 5 year , Rate = 10%Banker's Discount = FTR 100 Banker's Discount =3000 × 1 x 10 = Rs. 60 5 100