Interest rate time relationships – UGC NET Question

A is correct because compound interest at least matches and usually exceeds simple interest for the same principal, rate and time. B correctly gives the annual compounding formula, and C is true since in simple interest interest ∝ rate × time, so halving one and doubling the other keeps the product unchanged. E is also correct because more frequent compounding at a fixed nominal rate increases the effective annual rate. D is false because changing rate and time in that way does not guarantee the same accumulated amount. Therefore, A, B, C and E only are correct.

Option A:
Option A omits E and thus fails to mention the important concept of effective rate increasing with compounding frequency. Although A, B and C are true, the combination is incomplete and so not the best answer.

Option B:
Option B is correct since it gathers all the true statements and excludes D, which wrongly suggests invariance of amount under doubling rate and halving time in compound interest. It matches the standard treatment of interest problems in aptitude tests.

Option C:
Option C wrongly includes D, which misrepresents compound interest behaviour, and omits A, underplaying the comparison between compound and simple interest. Hence it mixes a false statement with an omission.

Option D:
Option D is incorrect as it includes D and discards B and C, thereby accepting the erroneous claim and omitting correct formulas and relationships.