Present worth of two equal half-yearly instalments: A total of Rs 702 is to be paid in two equal instalments due at the end of 6 months and 12 months respectively. If interest is 8% per annum (simple interest), find the present worth today of the two instalments combined.

Introduction / Context:
When a total amount is split into equal instalments due at different future times, the present worth (PW) is the sum of the discounted values of each instalment to today under simple interest.

Given Data / Assumptions:

• Total due in two instalments = Rs 702 → each instalment = Rs 351.
• Instalment due dates: 6 months and 12 months.
• Simple interest rate r = 8% p.a.

Concept / Approach:
Under simple interest, PW = F / (1 + r * t) for each cash flow, with t in years. Sum the two present values for the total PW.

Step-by-Step Solution:

Verification / Alternative check:
If invested today: 337.5 grows to 351 in 6 months at 8% p.a.; 325 grows to 351 in 12 months at 8% p.a. Sum at those due dates matches required instalments, validating the PW.

Why Other Options Are Wrong:
Values like 650, 640, 675 do not match the exact discounting of each instalment under the given rate and timings.

Common Pitfalls:
Discounting both instalments with the same time; using compound interest unintentionally; or dividing Rs 702 by 1.08 only (ignoring the 6-month instalment timing).

Final Answer:
Rs 662.50