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A sum of Rs 12,000 is invested at 10% per annum compound interest for 2 years. What will be the interest earned?
2,400
2,520
2,600
2,500
2,520
Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods, resulting in exponential growth. For an investment of Rs 12,000 at 10% interest for 2 years, the total amount is calculated as A=P(1+100RтАЛ)n, and the interest is the difference between this amount and the principal.
Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods, resulting in exponential growth. For an investment of Rs 12,000 at 10% interest for 2 years, the total amount is calculated as A=P(1+100RтАЛ)n, and the interest is the difference between this amount and the principal.
Think of compound interest like a snowball rolling down a hill; as it gathers snow (interest), its surface area increases, allowing it to collect even more snow (additional interest) with every subsequent rotation.
CI for Growth: Add the gain to the grain to get the gain again.
A=P(1+100RтАЛ)n тАФ Formula for the total amount including compound interest
CI=AтИТP тАФ Formula for compound interest earned
The principle relies on the property of compounding, where the interest earned at the end of the first year (12,000├Ч0.10=1,200) is added to the principal to form the new base for the second year. In the second year, interest is earned on both the initial principal and the first year's interest. This is effectively represented by the geometric progression of capital over discrete time intervals.
Simple interest remains constant for each period because it is only calculated on the initial principal.
Compound interest leads to exponential growth of the total amount over time.
As the number of compounding periods (n) increases, the interest earned grows at an increasing rate.
Maximizes wealth accumulation over long time horizons due to the compounding effect.
Increases the total debt burden significantly when applied to loans or credit card balances.
Investment portfolios and savings accounts
Amortization of home or personal loans
For 2 years at 10%, the effective interest rate is (1.10)2тИТ1=0.21 or 21%. 12,000├Ч0.21=2,520.
Option A (2,400) is the value for simple interest (12,000├Ч0.10├Ч2).
B is correct тАФ The compound interest earned is Rs 2,520, calculated by subtracting the principal from the total compounded amount after two years.
Always verify if the question asks for the 'Amount' (A) or just the 'Interest' (CI) to avoid picking the wrong final value.
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