The present worth (present value) of Rs. 169 due after 2 years at 4% per annum compound interest, compounded annually, is to be found. What is this present value?

Introduction / Context:
This is a classic present value question using compound interest. You are given a future sum (Rs. 169) that is due after a certain period, and you must compute how much should be invested today at 4% compound interest so that it grows to Rs. 169 in 2 years. This is central to topics such as time value of money and discounting.

Given Data / Assumptions:
- Future value (amount due after 2 years) = Rs. 169.
- Rate of interest = 4% per annum, compounded annually.
- Time period = 2 years.
- Let the present value (principal) be P rupees.
- We assume a standard compound interest environment with no additional deposits or withdrawals.

Concept / Approach:
For compound interest, the relationship between present value P and future value A is:
A = P * (1 + r/100)^n, where r is the annual rate and n is the number of years.
Here, A is known (169), r = 4, n = 2. We solve this formula for P by dividing A by (1.04)^2. This gives the amount that should be invested now to reach Rs. 169 in 2 years at 4% compound interest.

Step-by-Step Solution:
Step 1: Use the compound interest formula: A = P * (1 + 4/100)^2.Step 2: Substitute A = 169: 169 = P * (1.04)^2.Step 3: Compute (1.04)^2 = 1.0816.Step 4: Rearrange to find P: P = 169 / 1.0816.Step 5: Perform the division: P = 156.25.Step 6: Therefore, the present worth of Rs. 169 due in 2 years is Rs. 156.25.

Verification / Alternative check:
Check by forward calculation: invest Rs. 156.25 at 4% per annum. After 1 year, amount = 156.25 * 1.04 = 162.5. After 2 years, amount = 162.5 * 1.04 = 169. This matches the given future amount exactly, confirming that Rs. 156.25 is the correct present value.

Why Other Options Are Wrong:
Rs. 150 or Rs. 140, when grown at 4% compound interest for 2 years, will not reach Rs. 169, yielding lower final amounts. Rs. 125.25 is much too low and results in a far smaller future value. Rs. 160 is close but still incorrect; compounding 160 at 4% for 2 years gives less than Rs. 169. Only Rs. 156.25 grows exactly to Rs. 169 in 2 years at 4% C.I.

Common Pitfalls:
Learners often confuse simple and compound interest and might divide by (1 + 2 * 4/100) instead of (1.04)^2, or forget to square the factor. Another error is rounding prematurely, which can slightly distort the final present value. Always apply the compound factor correctly and, in exam-type questions, match to the nearest option given.

Final Answer:
The present worth of Rs. 169 due in 2 years at 4% compound interest is Rs. 156.25.