True Discount and Banker's Discount problems tricks

True Discount and Banker’s Discount problems short-tricks

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TRUE DISCOUNT AND BANKER’S DISCOUNT TRICKS IN HINDI

True Discount and Banker's Discount problems tricks

TRUE DISCOUNT

1). True Discount = Amount – Present worth
2). If the rate of interest is r% p.a., time t and present worth (PW), then the actual discount is-

    \[\frac{PW\times r\times t}{100}\]

3). If r% and money payable after time t is A, then the present worth is- 

    \[\frac{100\times A}{(100+r\cdot t)}\]

4). If the money payable on A is given at r% and time t, then the true discount is-

    \[\frac{A\times r\times t }{(100+r\cdot t)}\]

5). If after a certain period of time, at a fixed annual rate, the true discount (TD) on the money due and the simple interest (SI) for the same time and rate, then the money payable A is-

    \[\frac{SI \times TD}{(SI - TD)}\]

6). If t time after, the true discount (TD) and simple interest (SI) on the amount due at r% per annum, then

    \[SI - TD = \frac{TD\times r\times t}{100}\]

7). Money A’s present worth (PW) due after t years at r% compounded is-

    \[\frac{A}{\left(1+\frac{r}{100}\right)^t}\]

And the true discount is-

    \[A - PW\]

BANKER’S DISCOUNT

1). Banker’s discount = interest on the bill for the remaining time (unexpired time) =

    \[\frac{\text{bill amount} \times \text{rate} \times \text{unexpired time} }{100}\]

2). Banker’s profit = Banker’s discount – true discount
3). If the marked price of the bill is A, time t and rate is r%, then the Banker’s discount-

    \[\frac{A\times r\times t}{100}\]

4). At time t and rate r% on a bill of marked price A –
*. Banker’s profit =

    \[\frac{A(r\cdot t)^2}{100(100+r\cdot t)}\]

*. Banker’s profit =

    \[\frac{(TD)^2}{PW}\]

5). If the true discount on a bill payable after time t is TD, and the rate of interest per annum is r%, then the banker’s profit is-

    \[\frac{TD\times r\times t}{100}\]

6). If the marked price on the bill is A and the true discount is TD, then the banker’s discount

    \[\frac{A\times TD}{(A-TD)}\]

7). If the banker’s profit on a bill payable after time t at r% simple interest is BP, then the present worth (PW) is-

    \[BP\left(\frac{100}{r\cdot t}\right)^2\]

8). If the banker’s profit on a bill is BP and the present worth is PW, then the true discount (TD)-

    \[\sqrt{(PW\times BP)}\]

9). If banker’s discount (BD) and true discount (TD) is given on a bill, then the amount of bill A is-

    \[\frac{BD\times TD}{(BD-TD)} = \frac{BD\times TD}{BP}\]

10). If the banker’s discount on a sum a for a certain time at the rate of r% interest, and the true discount on a sum of b for the same rate and time is equal, then the value of time-

    \[\frac{100}{r\cdot \left(\frac{b-a}{a}\right)}\]

11). If the rate of interest and time on a bill are numerically equal, and the true discount is n times the banker’s discount, then the rate of interest or time

    \[10\sqrt{\left(\frac{1}{n}\right)}\]

Abbreviations to be noted

TD = True Discount
PW = Present worth
A = Amount
SI = simple interest
CI = Compound interest
BD = Banker’s Discount
BP = Bankers Profit

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