Statement 1: On a certain sum, at the same rate of interest and for the same time period, compound interest is always greater than the simple interest.

Statement 2: In compound interest, the principal remains constant for the whole time period, however the compound interest keeps increasing every year.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

On a certain sum, at the same rate of interest and for the same time period,

For a time period of one year, compound interest (CI) = simple interest (SI).

But for more than one year, CI is always greater than SI, because interest is added to the principal after each compounding period, increasing the amount on which interest is calculated.

On a certain sum, at the same rate of interest and for the same time period, compound interest is always greater or equal to the simple interest.

So, statement 1 is false.

In compound interest, the principal does not remain constant — it increases after each compounding period because interest is added to it.

So, statement 2 is false.

Hence, option 2 is the correct option.