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On a certain sum, at the same rate of interest, the simple interest is ₹120 and the compound interest is ₹126 for 2 years. What is the sum (in ₹)?
600
800
1000
1200
600
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years represents the interest earned on the interest from the first year. Since the total SI is ₹120 for 2 years, the interest for 1 year is ₹60, and the extra ₹6 (126 - 120) is the interest accrued on that ₹60.
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years represents the interest earned on the interest from the first year. Since the total SI is ₹120 for 2 years, the interest for 1 year is ₹60, and the extra ₹6 (126 - 120) is the interest accrued on that ₹60.
Think of Simple Interest as a fixed salary, while Compound Interest is like a growing plant where the flowers themselves produce seeds that bloom into new flowers the following year.
SI is linear, CI is exponential; the 'gap' is the interest's interest.
SI=100P×R×T — Simple Interest formula
Diff=1002P×R2 — CI and SI difference for 2 years
Rate=SI for 1 yearDifference×100 — Shortcut for rate
For a principal P and rate R, SI for one year is 100PR=60. The CI-SI difference for 2 years is calculated by the formula Diff=1002P×R2. Since 100PR=60, we substitute R to find P. Alternatively, the interest on the first year's interest (60) equals the difference (6), thus the rate R=(6/60)×100=10%. Substituting back, 100P×10=60, so P=600.
SI remains constant every year because it is calculated only on the principal.
CI increases over time because it is calculated on the principal plus accumulated interest.
The difference between CI and SI for 2 years is exactly the interest on the first year's interest.
The difference formula provides a rapid path to the principal without calculating full amounts.
This specific shortcut formula only applies directly to 2-year scenarios.
Banking sector for calculating returns on fixed deposits.
Analyzing debt accumulation and investment growth over time.
In this problem, R=10%.
Option B (800) would yield a difference of 8, Option C (1000) would yield 10, and Option D (1200) would yield 12.
A is correct — The sum is calculated as ₹600 by identifying the interest on the first year's simple interest.
Whenever given SI and CI for 2 years, always find the interest on one year's SI first to determine the rate of interest immediately.
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