Question

Suppose for the principal \( P \), rate \( R% \), and time \( T \), the simple interest is \( S \) and the compound interest is \( C \). Consider the possibilities:

• A. \( C > S \)
• B. Only (i) is correct
• C. Either (i) or (ii) is correct
• D. Either (ii) or (iii) is correct

Hint:

Always compare simple and compound interest using the formula to determine their relationship. Compound Interest is usually greater when compounded over multiple years.

Answer 1

The Correct Option is B

Step 1: Understanding the relationship between Simple and Compound Interest
- Compound Interest (CI) is generally greater than Simple Interest (SI) when the interest is compounded annually or more frequently. That is, \( C < S \).
- If the time period is very small (e.g., one year) or the rate is extremely low, CI and SI can be approximately equal, i.e., \( C = S \).
- However, \( C \) is never less than \( S \) in normal circumstances.
Step 2: Evaluating the given statements
- Statement (i) \( C < S \) is generally true for most cases.
- Statement (ii) \( C = S \) is possible when the time period is very short or for extremely low interest rates.
- Statement (iii) \( C < S \) is incorrect because CI is always equal to or greater than SI.
Thus, either (i) or (ii) is correct.