The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 26. Find the present worth.

Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 26. Find the present worth.

Solution:
Banker Gain = 26
True Discount = (Bnakers gain × 100)/(rate × time) = (26 × 100)/(10 × 2) = 130

Banker's Gain = Banker's Discount - True discount
⇒ 26 = Banker's discount - 130
∴ Banker's discount = 130 + 26 = 156

Now, banker's discount is the interest on the face value
Let the face value = x
So,
x × (10/100) × 2 = 156
⇒ x × 0.1 × 2 = 156
⇒ x = 156/0.2 = 780

Now,
Present Worth = Face value - True discount
= 780 - 130
= 650