The true discount on Rs. 2,562 due 4 months hence is Rs. 122. Find the annual simple interest rate.

Given data

• A = Rs. 2,562
• TD = Rs. 122
• t = 4 months = 1/3 year

Concept

TD = A × (r t) / (1 + r t). Let y = r/3.

Steps
122 = 2562 × y / (1 + y)122 + 122y = 2562y ⇒ 122 = (2562 − 122)y = 2440yy = 122/2440 = 0.05 ⇒ r = 3y = 0.15 = 15% p.a.

Final Answer
Rate = 15% per annum.