What is the present value of ₹169 due in 2 years if money is compounded annually at 4% per annum? (That is, how much should be invested today to get ₹169 after 2 years at 4% compounded annually?)

Introduction:
This question tests present value under compound interest. Present value is the amount that, when compounded at a given rate for a given time, becomes the future value. With annual compounding, we use PV = FV / (1 + r/100)^t. Here the future value is ₹169, rate is 4% per annum, and time is 2 years, so we compute the discount factor and divide.

Given Data / Assumptions:

• Future value FV = ₹169
• Rate r = 4% per annum compounded annually
• Time t = 2 years
• Present value formula: PV = FV / (1 + r/100)^t

Concept / Approach:
Compute compound growth factor for 2 years: (1.04)^2. Then divide the future value by this factor to get the present value. Since compounding is annual, no conversion of periods is needed.

Step-by-Step Solution:
PV = FV / (1 + r/100)^t PV = 169 / (1 + 4/100)^2 PV = 169 / (1.04)^2 (1.04)^2 = 1.0816 PV = 169 / 1.0816 = 156.25

Verification / Alternative check:
Check by compounding: 156.25 * 1.04 = 162.50 (after 1 year). Then 162.50 * 1.04 = 169.00 (after 2 years). The result matches exactly, confirming the present value is correct.

Why Other Options Are Wrong:
₹158.00 and ₹160.25 are too high and would compound to more than ₹169. ₹150.50 and ₹154.75 are too low and would compound to less than ₹169. Only ₹156.25 compounds to exactly ₹169 in 2 years at 4%.

Common Pitfalls:
Using simple interest discounting instead of compound discounting, forgetting to square the growth factor for 2 years, or using 0.04 incorrectly while also dividing by 100 again.

Final Answer:
The present value is ₹156.25.