Present Worth under Compound Interest – Discount a future amount at 4%: What is the present worth of ₹ 169 due in 2 years at 4% per annum compounded annually?

Introduction / Context:
Discounting is the reverse of compounding. Present worth finds today’s equivalent of a known future amount by dividing by the appropriate growth factor. Here, we discount ₹ 169 due after 2 years at 4% compounded annually.

Given Data / Assumptions:

• Future amount F = 169 in 2 years
• Rate r = 4% per annum
• Compounding annually

Concept / Approach:
Present value PV = F / (1 + r)^t. Substitute F = 169, r = 0.04, t = 2. Compute (1.04)^2 accurately to ensure an exact match with standard values used in exam questions.

Step-by-Step Solution:
(1.04)^2 = 1.0816PV = 169 / 1.0816 = 156.25

Verification / Alternative check:
Forward check: 156.25 grown for 2 years at 4% yields 156.25 * 1.0816 = 169, confirming exact equivalence.

Why Other Options Are Wrong:
₹ 160 and ₹ 158 are approximations that do not reproduce ₹ 169 after compounding; ₹ 154.75 and ₹ 150.50 understate the required present value.

Common Pitfalls:
Applying simple discounting instead of compound discounting produces slightly different results; ensure you divide by the compounded factor, not 1 + r * t.

Final Answer:
₹ 156.25