Present worth to discharge a future debt: What sum paid now will discharge a debt of Rs. 5300 due 1.5 years hence at 4% per annum simple interest?

Introduction / Context:The present worth (true discount method) finds today’s payment that is exactly equivalent, under simple interest, to a specified future amount. This is classic time-value-of-money under simple interest, using the formula PW = A / (1 + r * t).

Given Data / Assumptions:

• Future amount A = 5300.
• Time t = 1.5 years.
• Rate r = 4% per annum simple.

Concept / Approach:Apply PW = A / (1 + r * t). The true discount TD equals A − PW if needed, but here only PW is asked (the sum to discharge the debt now).

Step-by-Step Solution:PW = 5300 / (1 + 0.04 * 1.5) = 5300 / (1 + 0.06) = 5300 / 1.06 = 5000.

Verification / Alternative check:Accruing 5000 for 1.5 years at 4%: 5000 * (1 + 0.04 * 1.5) = 5000 * 1.06 = 5300, matching the due amount exactly.

Why Other Options Are Wrong:

• 4500 and 4200 underpay today; they would not grow to 5300 at 4% over 1.5 years.
• 5250 is too high; growing to 5565, which exceeds the due amount.

Common Pitfalls:

• Using banker’s discount (A − A * r * t) instead of present worth division; both differ for finite time.

Final Answer:Rs. 5000