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The difference between Simple Interest and Compound Interest on a sum of ₹10,000 for 2 years at 10% per annum is:
50
100
150
200
100
Simple Interest (SI) is calculated only on the principal amount, whereas Compound Interest (CI) is calculated on the principal plus the accumulated interest. For a 2-year duration, the difference arises because CI includes interest earned on the interest from the first year.
Simple Interest (SI) is calculated only on the principal amount, whereas Compound Interest (CI) is calculated on the principal plus the accumulated interest. For a 2-year duration, the difference arises because CI includes interest earned on the interest from the first year.
Simple interest is like planting a static tree that produces the same number of fruits yearly, while compound interest is like planting a tree whose fruits drop seeds that sprout into new, fruit-bearing trees themselves.
For 2 years, use the square rule: D=P(100R)2.
SI=100P×R×T — Simple Interest formula
CI=P(1+100R)T−P — Compound Interest formula
Difference=P×(100R)2 — Difference formula for T=2 years
The principle relies on the power of compounding. SI grows linearly at a rate of SI=100P×R×T, whereas CI grows exponentially, defined by A=P(1+100R)T. The difference for two years simplifies to CI−SI=P×(100R)2.
Simple interest remains constant for each period.
Compound interest increases progressively due to the addition of interest to the principal.
The difference for two years is exactly the interest earned on the interest of the first year.
Compound interest maximizes wealth accumulation over time.
Simple interest is easier to calculate and predict for short-term debt.
Compound interest makes debt significantly harder to pay off if not managed early.
Bank savings accounts and investments
Loan amortization and credit card debt
For P=10000, R=10%, T=2: SI=2000, CI=2100. Difference = 100.
Option A is ₹50 (incorrect, ignores the compounding effect correctly), Option C is ₹150, Option D is ₹200.
B is correct — The difference arises from the interest earned on the first year's interest, which amounts to 10000×(0.1)2=100.
Always verify if the interest is compounded annually, semi-annually, or quarterly, as this changes the effective rate (R) and time (T) in the formulas.
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