What is the present worth of Rs. 169 due in 2 years at 4 percent per annum compound interest, compounded annually?

Introduction / Context:
Present worth or present value is a key concept in compound interest problems. Instead of finding the amount after a certain time, we are given the future amount and asked to find how much should be invested today. This question tests the ability to reverse the compound interest process using the appropriate formula and to interpret results accurately in terms of money.

Given Data / Assumptions:

• Future amount due in 2 years = Rs. 169.
• Rate of interest = 4 percent per annum compound interest.
• Compounding is done annually.
• We must find the present worth, that is the principal that would grow to Rs. 169 in 2 years at the given rate.

Concept / Approach:
The compound amount formula is: A = P * (1 + r/100)^n where A is the amount, P is the principal, r is the rate, and n is the number of years. To find present worth P when A is given, we rearrange the formula: P = A / (1 + r/100)^n We substitute A = 169, r = 4, and n = 2 and simplify to get the present value.

Step-by-Step Solution:
Given A = Rs. 169 Rate r = 4 percent per annum Time n = 2 years P = A / (1 + r/100)^n 1 + r/100 = 1 + 4/100 = 1.04 (1.04)^2 = 1.04 * 1.04 = 1.0816 P = 169 / 1.0816 Compute: 169 / 1.0816 = 156.25 Therefore, the present worth is Rs. 156.25

Verification / Alternative check:
We can verify the result by compounding Rs. 156.25 forward for 2 years at 4 percent. After 1 year: 156.25 * 1.04 = 162.50 After 2 years: 162.50 * 1.04 = 169.00 We reach exactly Rs. 169, which matches the given future amount. This confirms that our present value calculation is correct.

Why Other Options Are Wrong:
Rs. 150 and Rs. 140 are too low; when compounded at 4 percent for 2 years they will not reach 169. Rs. 125.25 is much smaller and clearly would not grow to 169 at such a modest rate. Rs. 160 is closer, but if we compound 160 for 2 years at 4 percent, we get: 160 * 1.04 * 1.04 = 160 * 1.0816 = 173.06 which is higher than 169. Only Rs. 156.25 compounds exactly to Rs. 169 under the given conditions.

Common Pitfalls:
A common mistake is to treat the problem like simple interest and divide by (1 + r * n / 100) instead of by the proper compound factor. Some students also forget to square the factor (1.04) for 2 years and only divide by 1.04 once. Rounding too early in intermediate steps can also produce small errors. Using the formula carefully and checking by recomputing the forward amount helps avoid these issues.

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