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Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of both the sums was 2 years and rate of interest too was same 10% per annum. At the end, he found a difference of тВ╣97 in both the interests received. What were the sums (in тВ╣) invested?
8,950
8,800
9,700
10,050
9,700
The difference between Compound Interest (CI) and Simple Interest (SI) for a principal P over 2 years at a rate R is given by the formula D=P├Ч(100RтАЛ)2. Given D=97 and R=10, the principal is calculated as P=97├Ч(10100тАЛ)2=9,700.
The difference between Compound Interest (CI) and Simple Interest (SI) for a principal P over 2 years at a rate R is given by the formula D=P├Ч(100RтАЛ)2. Given D=97 and R=10, the principal is calculated as P=97├Ч(10100тАЛ)2=9,700.
Think of Simple Interest as a fixed salary, while Compound Interest is like a snowball rolling down a hill that picks up more snow (interest) every time it makes a turn.
SI=100P├ЧR├ЧTтАЛ тАФ Simple Interest formula
CI=P(1+100RтАЛ)TтИТP тАФ Compound Interest formula
D=P├Ч(100RтАЛ)2 тАФ Difference for 2 years
Simple interest is calculated only on the initial principal, whereas compound interest is calculated on the principal plus the accumulated interest from previous periods. In the second year, the compound interest earns an additional 'interest on interest' equal to the interest of the first year's interest. This difference is effectively P├Ч(100RтАЛ)├Ч(100RтАЛ).
For 2 years, the difference between CI and SI is always the interest earned on the first year's interest.
The interest rate must be in percentage, so 100RтАЛ represents the decimal fraction.
Compounding annually means interest is added to the principal once per year.
Compound interest grows exponentially, providing higher returns over time compared to simple interest.
Simple interest remains linear and does not benefit from the accumulation of previous interest gains.
Banking savings accounts
Loan amortizations and debt management
| Feature | Simple Interest | Compound Interest |
|---|---|---|
Growth Pattern | Linear | Exponential |
At 10% rate for 2 years, SI = 20% of P and CI = 21% of P, leading to a difference of 1% of P.
Option C is 9,700. If we take 1% of 9,700, we get 97, which matches the problem statement.
C is correct тАФ The difference of 97 between CI and SI for 2 years at 10% rate corresponds to a principal amount of 9,700.
Always check if the interest is compounded annually or semi-annually; for semi-annual compounding, the rate is halved and time is doubled.
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