Compound amount general formula – UGC NET Question

This option is correct because the standard formula for compound interest with annual compounding is A = P(1 + r/100)^n. The factor (1 + r/100) represents the growth factor for one year. Repeating it n times corresponds to compounding the interest every year. Therefore, this expression correctly gives the amount after n years.

Option A:
The expression P(1 + nr/100) resembles simple interest growth, not compound interest. It assumes interest grows linearly with time instead of exponentially. Thus, it does not represent annual compounding and is not correct here.

Option B:
The formula P(1 + r/100)^n multiplies the principal by the growth factor once for each year. This matches the compounding process, where each year's interest is calculated on the new amount. Hence, this option is the correct compound interest formula.

Option C:
The expression P(1 − r/100)^n models a decreasing quantity, such as depreciation, where a fixed percentage is lost each year. It is not appropriate when interest is added rather than subtracted. Therefore, it does not answer the question.

Option D:
The term P(1 − nr/100) assumes a linear decrease in the amount with time, which again is not how compound interest works. It would eventually make the amount zero or negative for large n, which is unrealistic for interest growth. Hence, this option is incorrect.