The true discount on a bill due 9 months hence at 16% p.a. is Rs. 189. Find the amount (face value) of the bill.

Given data

• TD = Rs. 189
• Rate r = 16% p.a.
• Time t = 9 months = 0.75 year
• Let amount = A

Concept

TD = A × (r t) / (1 + r t).

Steps
r t = 0.16 × 0.75 = 0.12189 = A × 0.12 / 1.12 ⇒ A = 189 × (1.12 / 0.12) = 1,764

Final Answer
Bill amount = Rs. 1,764.