Discussion
The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:
Answer: A
Rs. 1404 is paid in two equal half-yearly installments, so each installment is Rs. 702 - one due in 6 months, the other in 12 months. Discount each separately.
First installment (\( T = 0.5 \) year at 8%):
\[ \text{PW}_{1} = \frac{702}{1 + 0.04} = \frac{702}{1.04} = 675 \]
Second installment (\( T = 1 \) year):
\[ \text{PW}_{2} = \frac{702}{1 + 0.08} = \frac{702}{1.08} = 650 \]
\[ \text{Total PW} = 675 + 650 = \text{Rs. } 1325 \]
Discounting the whole Rs. 1404 for a single average period gives a different (and wrong) figure - each installment must be discounted for its own waiting time.
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