Difficulty: Medium
Correct Answer: Rs.156.25
Explanation:
Introduction / Context:
This is a present value question using compound interest. You are told the future value (Rs. 169) that will be due in 2 years and the annual compound interest rate. The task is to find the amount that must be invested today to grow to that future value.
Given Data / Assumptions:
Concept / Approach:
For compound interest, the amount after T years is A = P * (1 + R / 100)^T. To find the present value, rearrange this to P = A / (1 + R / 100)^T. Substitute the known values of A, R, and T to obtain P.
Step-by-Step Solution:
Step 1: Write the compound amount formula: A = P * (1 + R / 100)^T.
Step 2: Rearrange for P: P = A / (1 + R / 100)^T.
Step 3: Substitute A = 169, R = 4, T = 2.
Step 4: Compute (1 + R / 100) = 1 + 4 / 100 = 1.04.
Step 5: Raise to the power T: (1.04)^2 = 1.0816.
Step 6: Calculate P = 169 / 1.0816.
Step 7: 169 / 1.0816 = 156.25, so the present value is Rs. 156.25.
Verification / Alternative check:
Verify by compounding Rs. 156.25 at 4% for 2 years. Year 1 amount = 156.25 * 1.04 = 162.5. Year 2 amount = 162.5 * 1.04 = 169. Thus, investing Rs. 156.25 now at 4% compounded annually will indeed accumulate to Rs. 169 in 2 years.
Why Other Options Are Wrong:
Rs.150.50, Rs.154.75, and Rs.158 would each grow to amounts less or more than Rs. 169 when compounded at 4% for 2 years, so they are not the correct present value.
Common Pitfalls:
Some learners mistakenly apply the simple interest formula instead of compound interest, or they forget to square the growth factor because T = 2 years. Another common issue is rounding too early. Doing the calculation carefully and only rounding at the final step helps avoid such errors.
Final Answer:
The present value of Rs. 169 due in 2 years at 4% compound interest is Rs.156.25.
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