The total amount due is Rs 1404, payable in two equal half yearly instalments, and the rate of simple interest is 8 percent per annum. What is the present worth (present value) of these two instalments together?

Introduction / Context:
This problem deals with the present value of instalment payments under simple interest. The total amount Rs 1404 is to be paid in two equal half yearly instalments. The task is to find the present worth of these two instalments when discounted at 8 percent per annum simple interest. Such questions are useful for understanding how instalment loans and present value calculations work.

Given Data / Assumptions:
- Total amount due = Rs 1404 in two equal half yearly instalments.
- Therefore each instalment is 1404 / 2 = Rs 702.
- Rate of interest r = 8 percent per annum simple interest.
- First instalment is due in 6 months, that is 0.5 years from now.
- Second instalment is due in 1 year from now.
- We must find the sum of the present values of both instalments.

Concept / Approach:
Under simple interest, the present value P of an amount A due after t years at rate r percent is P = A / (1 + r * t / 100). We calculate the present value of each instalment separately using its respective time until due, and then add the two present values. The sum of these present values is the present worth of the total payment schedule.

Step-by-Step Solution:
Step 1: Each instalment amount is A = 1404 / 2 = Rs 702. Step 2: Rate r = 8 percent per annum. Step 3: First instalment time t1 = 6 months = 0.5 years. Step 4: Second instalment time t2 = 1 year. Step 5: Present value of first instalment P1 = 702 / (1 + 8 * 0.5 / 100) = 702 / (1 + 4 / 100) = 702 / 1.04. Step 6: Present value of second instalment P2 = 702 / (1 + 8 * 1 / 100) = 702 / 1.08. Step 7: Compute P1 ≈ 702 / 1.04 = 675. Step 8: Compute P2 ≈ 702 / 1.08 = 650. Step 9: Total present worth = P1 + P2 = 675 + 650 = Rs 1325.

Verification / Alternative check:
To verify, if we take the present worth of Rs 1325 and spread it into two instalments with simple interest, we should reach the original amounts. Investing 675 at 8 percent for 0.5 years gives interest 675 * 8 * 0.5 / 100 = 27, so amount becomes 702. Investing 650 at 8 percent for 1 year gives interest 650 * 8 / 100 = 52, so amount becomes 702 again. This confirms that the present values 675 and 650 are correct and that their sum 1325 is indeed the present worth.

Why Other Options Are Wrong:
Options 1320, 1300 and 1200 do not reproduce the exact instalment amounts of 702 each under 8 percent simple interest for 0.5 year and 1 year. Only 1325, when split appropriately, grows to exactly 702 and 702.

Common Pitfalls:
Learners sometimes treat the total 1404 as a single payment and discount it once, instead of separating the instalments and discounting each at its own time. Another error is to use compound interest formulas where simple interest is specified. Always calculate present value separately for each instalment if the due dates are different.

Final Answer:
The present worth of the two instalments is Rs 1325.