Aptitude - Banker's Discount - Discussion

@All.

Explanation of what is BG(Bankers gain), TD(True discount), BD(Bankers discount)
Example:

A Sales BIKE worth of 12000 to B with agreement. In agreement B took 3 month time for payment. Due to some problem A needs money after one month. While that time B Gave that agreement to bank and borrow money.

A simply not give 3 months of time he put some interest say 10% per anum.
Hence - use PTR/100 formula we get interest -300,
One month is over so bank pay 12100 to A,
TD = 12300 - 12100= 200.
Bank also needs some profit so bankers put interest on total amount {12000+300(interest)} =12300.

Let's calculate interest using - PTR/100.

While calculating interest take T - 2 month because already one month is over.
After calculation we get - 205 rupees is BANK DISCOUNT.
Bank Gain = B.D - T.D = 205 - 200 = 5 rupees.

-> True discount means the simple interest obtained after the nominal date.

-> If one wants to withdraw money before the due date then banker will deduct some amount from the face value and give i.e one will get less than the face value amount.

-> Suppose x is the face value,if one withdraws after due date he will get (face value + interest),->i.e true discount.

-> If one withdraws before the due date then he will get (face value-some amount)(it some amount it may be equal to S.I)->i.e bankers discount.

-> Therefore,Banker's Gain= True discount-Bankers discount.

Following is explanation, and may be a shortcut for few students:

Banker's Discount (BD) is simple interest on Face Value of Bill (F).

Given that, BD = Rs. 420, Time (T) = 4/12 year, Interest Rate (R) = 0.15.

True Discount (TD) is simple interest on Present Worth (PW).

We know, BD = F*T*R/100 = 420.

=> F = BD*100/T*R .
=> F = 420*100*12/(4*15).
=> F = 420*20.

We know, PW = F/{1+(T*R/100)}
=> PW = 420*20*100/105.
=> PW = 4*20*100.

We know, TD = PW*T*R/100.
=> TD = 4*20*100*4*15/(100*12).
=> TD = Rs. 400.

Thanks.

I think it will be too much easy if we take this as present value and future value.
Here banker's discount on a bill due 4 months hence at 15 % is RS 420, this 420 is the future value which we will get after 4 months. But what is the present value of that 420 is the true discount and the required answer.

So we can solve it solve it in Pv formula where,

PV = FV /(1+rn).
= 420 /1+ (15/100 * 4/12),
= 420 * 100/105,
= 400.

we can also take it as amount which is 420.
so P = 420 * 100/ (n*r)+100,
= 420 * 100/105,
= 400.

Actually BD=amt*rate*time/100.

TD=amt*rate*time/100+(rate*time).
BD *100=amt*rate*time.
we are substituting the amt*rate*time in TD with BD*100 from the above step,
so TD=BD*100/100+(rate*time).
so TD=420*100/100+(15*1/3).
We write 4 months as 1/3 because the time should be expressed in terms of years,so 4/12=1/3.
Thus we get 420*100/105=400.

Hope this helps.

How comes this formula T.D. = B.D. x 100 / 100+(R*T)


Atually T.D = Amout*rate*time / 100+(R*T)

--------------------------------------------------------------------------------
B.D = amount*rate*time/100

T.D = (amount*rate*time/100)*100/100+(rate*time)
= amount*rate*time/100+(rate*time)

B.D = Banker's Discount.
T.D = True Discount.
A = Amount.
R = Rate.
T = Time.

T.D=A*R*T/(100+RT).

B.D=A*R*T/100.

Divide by 100 in numerator and denominator In T.D.

T.D=[(A*R*T)/100]/[(100+RT)*100].

In T.D formula substitute B.D formula.

T.D=[B.D*100]/[100+(R*T)].

Hi, all.

The true discount is initial amount Rs.400 (deposit on bank).

The banker's discount is the sum of amount and interest of the amount at particular interest rate (15%).

Rs.420 = 400 + (400x.15x(1/3)) = 400+20.

Somebody, please explain why TD formula 3time, and when to use, how to use it?

Before solving this question, I saw formulas but TD has three different way, confused and as per the TD FORMULA how 100 comes in formula?

Thanks @Kiran for explaining but I have a small doubt you said true discount is equal to simple interest.

But you said again is equal to face value+ simple interest. I didn't understand once explain that.