Discussion
The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:
Answer: A
Two equal half-yearly installments of Rs. 702 each - one due in 6 months, the other in 12 - must be discounted separately for their own waiting times.
\[ \text{PW}_{1} = \frac{702}{1 + \dfrac{8 \times 0.5}{100}} = \frac{702}{1.04} = \text{Rs. } 675 \]
\[ \text{PW}_{2} = \frac{702}{1 + \dfrac{8 \times 1}{100}} = \frac{702}{1.08} = \text{Rs. } 650 \]
\[ \text{total} = 675 + 650 = \text{Rs. } 1325 \]
Discounting the whole Rs. 1404 for a single averaged period does not give the same answer, because discounting is not linear in time.
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