Present worth with fractional time: What is the present worth of Rs. 272.61 due in 2 years 73 days at 7 1/2% per annum simple interest? (Assume 365 days in a year.)

Introduction / Context:
Present worth calculation with simple interest and a non-integer time requires converting the extra days into a fraction of a year. Then apply PW = S / (1 + r t). Careful handling of the day fraction ensures accuracy.

Given Data / Assumptions:

• S = Rs. 272.61 due after 2 years and 73 days.
• r = 7.5% per annum = 0.075.
• Year length assumed = 365 days.

Concept / Approach:
Convert 73 days to 73/365 years. Total t = 2 + 73/365 = 2.2 years. Then PW = 272.61 / (1 + 0.075 * 2.2).

Step-by-Step Solution:

Verification / Alternative check:
Re-accumulate: 234 * 1.165 = 272.61, confirming exactness to the paise.

Why Other Options Are Wrong:
Rs. 254 and Rs. 240 are too high; Rs. 334 is far off; “None of these” is unnecessary because an exact match exists.

Common Pitfalls:
Using 360 days instead of 365 without instruction, or omitting the 73-day fraction entirely.

Final Answer:
Rs. 234