Aptitude - Banker's Discount - Discussion

What is T.D , P.W , B.G?

can any body explain how is d formula obtained?

P.W is Present Worth. B.G is Bankers Gain.

T.D is True Discount

This formula is obtained by the banker gain formula i.e B.G=[T.D]*[T.D]/P.W

What does present worth mean?

How formula is obtained ?

How these all formulas on bankers discount and true discount are obtained? ate they baseless. Is there any existence of these type of formula in mathematics?

Following is explanation:

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

=> BD = F*R*T/100.

We know, Banker's Gain (BG) is difference between Banker's Discount (BD) and True Discount (TD).

=> BG = BD - TD.
=> 16 = BD - TD....equation (1).

Given that,

Present Worth (PW) = Rs. 576.

True Discount (TD) is to be found out, which is simple interest on Present Worth (PW).

We know that,

=> TD = PW*T*R/100.
=> TD = 576*T*R/100....equation (2).

From equation (1) & (2),

=> 16 = (F*R*T/100) - (576*T*R/100).
=> 16 = (F-576)*(R*T/100)....equation (3).

We know, PW = F/[1+(T*R/100)].

=> PW*[1+(T*R/100)] = F.
=> 576*[1+(T*R/100)] = F.

=> [1+(T*R/100)] = F/576.
=> (T*R/100) = (F/576)-1.

=> (T*R/100) = (F-576)/576....equation (4).

From equation (3) & (4),

=> 16 = (F-576)*(F-576)/576.
=> 16*576 = (F-576)*(F-576).

=> square root of (16*576) = (F-576).
=> 576±96 = F.

=> F = 672 or 480.

We take, F = 672.

From equation (2) & (4),

=> TD = 576*{(F-576)/576}.
=> TD = 672-576 = Rs. 96.

Here, F = 480 is not taken otherwise, TD would be negative.

Thanks.