The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

Question: The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

Solution:
PW = Tk. 1800
TD = Tk. 180

PW (present worth) = FV (face value) - TD (true discount)
⇒ Face value = present worth + true discount
= 1800 + 180
= 1980

True discount is the simple interest on the present value for the unexpired time.
Now, simple interest on Tk. 1800 for unexpired time = Tk. 180
The rate of simple interest = (180/1800) × 100% = 10%

Banker's discount is the simple interest on the face value of the bill for unexpired time.
simple interest on Tk. 1980 for unexpired time or remaining time.
R = 10%
Banker's discount = 1980 × (10/100) = 198

Banker's gain = Banker's discount - True discount
= 198 - 180
= 18

Alternative Solution:
Banker's gain = (True discount)²/Present worth
= (180)²/1800
= 18