Discussion

The present worth of Rs.1404 due in two equal half-yearly instalments at 8% per annum. Simple interest is:

Answer: C

The Rs. 1404 comes as two equal installments of Rs. 702, one due in 6 months and one in 12, so each is discounted for its own period.

\[ \text{PW}_{1} = \frac{702}{1 + \dfrac{8 \times 0.5}{100}} = \frac{702}{1.04} = \text{Rs. } 675 \]

\[ \text{PW}_{2} = \frac{702}{1 + \dfrac{8 \times 1}{100}} = \frac{702}{1.08} = \text{Rs. } 650 \]

\[ \text{present worth} = 675 + 650 = \text{Rs. } 1325 \]

Discounting the full Rs. 1404 for an averaged 9 months gives Rs. 1324.5 - close, but not equal, because discounting is not linear in time.

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