Compound Interest – Find time at 4% per annum from two amounts: In what time will ₹ 390,625 amount to ₹ 456,976 at 4% compound interest (annual compounding)?

Introduction / Context:
Given initial and final amounts under a fixed compound rate, the time can be deduced by matching the ratio A/P to integer powers of the annual growth factor. This avoids logarithms when the data are designed to align with neat powers.

Given Data / Assumptions:

• P = 390,625
• A = 456,976
• Annual rate r = 4% ⇒ factor per year = 1.04

Concept / Approach:
Compute A/P and compare to powers of 1.04: 1.04^2 = 1.0816; 1.04^3 ≈ 1.124864; 1.04^4 ≈ 1.16985856. If A/P equals 1.16985856, time is 4 years.

Step-by-Step Solution:
A/P = 456,976 / 390,625 ≈ 1.16985856Recognize that 1.16985856 = (1.04)^4Hence, time t = 4 years

Verification / Alternative check:
Forward compute: 390,625 * (1.04)^4 = 390,625 * 1.16985856 = 456,976 exactly (these are perfect power/pair values often used in exams).

Why Other Options Are Wrong:
2, 3, or 5 years correspond to different powers of 1.04 that do not hit the exact ratio 456,976 / 390,625.

Common Pitfalls:
Rounding too early may cause mismatch; use exact or high-precision values for powers of 1.04 to spot the correct integer exponent.

Final Answer:
4 years