Discussion
What is the present worth of ₹2,600 due 2 years 6 months hence at 12% per annum?
Answer: B
Correct answer: ₹2,000
The present worth is the sum which, invested now at simple interest, would amount to the face value at maturity: \[ \text{PW} = \frac{100 \times A}{100 + RT}. \] Here \( R = 12 \) and \( T = 2.5 \) years, so \( RT = 30 \). Then \[ \text{PW} = \frac{100 \times 2600}{130} = \frac{260000}{130} = 2000. \] Checking forwards: 2,000 at 12% for two and a half years earns \( 2000 \times 0.30 = 600 \) in interest, giving exactly 2,600 at maturity. The true discount is that 600, being the difference between the face value and the present worth. The relation \( A = \text{PW} + \text{TD} \) holds always, and it is the quickest check on any answer in this topic.
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