The true discount on a sum due 2 years hence at 14% p.a. is Rs. 168. What is the sum due?

Concept / Approach

• With simple interest, for an amount A due after t years at r% p.a.:

Present worth P = A / (1 + rt/100)True discount TD = A − P = A × (rt)/(100 + rt)

Step-by-step calculation
Here t = 2, r = 14 ⇒ rt = 28TD = A × 28/(100 + 28) = A × 28/128 = A × 7/32168 = A × 7/32 ⇒ A = 168 × 32/7 = 768

Verification
Present worth P = 768 × 100/128 = 600; SI on Rs. 600 for 2 years at 14% = 600 × 14 × 2 / 100 = 168 = TD ✔

Final Answer
Rs. 768