UGC NET Questions (Paper – 1)

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.

Compound interest for 2 years at 10% per annum is computed using the amount formula A = P(1 + R/100) raised to the power of time. Here, A = 10,000 × (1 + 10/100)² = 10,000 × (1.1)². The value of (1.1)² is 1.21, so the amount becomes 10,000 × 1.21 = 12,100. The compound interest is the amount minus the principal, which is 12,100 − 10,000 = ₹2,100.

Option A:
Option A, ₹1,000, equals simple interest for one year at 10% but fails to account for the interest-on-interest effect in the second year. It underestimates the total interest earned over two years.

Option B:
Option B, ₹2,000, corresponds to simple interest over two years (10% each year on the principal only), but compound interest is slightly higher because the second year’s interest is also earned on the first year’s interest.

Option C:
Option C correctly derives the amount using the compound interest factor (1.1)² and subtracts the original principal. This procedure captures the compounding process and yields the slightly larger interest of ₹2,100.

Option D:
Option D, ₹2,200, overstates the effect of compounding and would require a higher effective rate or more time than actually given in the problem.

Statements A, B, C and D together give a complete and correct conceptual comparison of simple and compound interest in exam-type settings. A is correct for positive rates and more than one year because compounding on accumulated amounts cannot yield less than simple interest on principal. B and C correctly distinguish the bases on which interest is calculated in the two regimes, and D accurately contrasts the linear versus exponential-type growth patterns. Statement E is false because for exactly one year simple and compound interest coincide, so simple interest is not greater, and hence the correct combination must include A, B, C and D but exclude E.

Option A:
Option A is correct because it captures all of the true statements and omits E, which misstates the one-year comparison between simple and compound interest. It recognises that compounding over multiple periods increases or at least matches simple interest and that the two schemes use different bases for interest calculation. It also correctly reflects the different shapes of the time–amount graphs.

Option B:
Option B is incorrect because it leaves out D, the key statement about linear versus exponential-like growth, so the description of time behaviour is incomplete. Although A, B and C are true, this combination does not fully convey how amounts diverge over longer periods. For conceptual NET questions, missing such a central point makes the option inadequate.

Option C:
Option C is wrong because it includes E along with otherwise correct statements; E wrongly claims that simple interest is always greater than compound interest for one year. Including even one false statement makes the whole set incorrect in a “select correct statements” question. Therefore this combination cannot be accepted as correct.

Option D:
Option D is incorrect because it omits A and D while still containing E, the false statement. By dropping A it loses the general comparison between the two interest types, and by adding E it introduces an error about the one-year case. This mixture of omission and error makes the option invalid.

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.

For compound interest compounded annually, the amount A after n years is A = P(1 + R/100)^n. Substituting P = 5000, R = 10 and n = 2 gives A = 5000(1.1)^2 = 5000 × 1.21 = 6050. This includes both the principal and the accumulated interest over 2 years. Therefore, the amount after 2 years is ₹6050.

Option A:
₹6050 is correct because it reflects a 10% increase in the first year to ₹5500 and another 10% increase on ₹5500 in the second year, giving an interest of ₹550 in the second year. Adding the two years’ interest, 500 + 550 = 1050, to the principal yields 6050. This step-by-step reasoning confirms the formula-based calculation.

Option B:
₹6000 would correspond to a simple interest of ₹1000 over 2 years at 10% per annum, ignoring compounding in the second year. Compound interest, however, adds interest on both principal and accumulated interest. Therefore, 6000 underestimates the true amount.

Option C:
₹5900 is even smaller than the simple interest amount and thus significantly underestimates the effect of compound growth. It does not arise from any standard calculation with the given rate and time. Hence, this option is incorrect.

Option D:
₹6100 overestimates the compound amount at 10% per annum on ₹5000 for 2 years. It might result from an incorrect assumption of a higher effective rate. Since the exact formula yields 6050, 6100 cannot be accepted as correct.

For compound interest, the amount is given by A = P(1 + R/100)ᵗ. Here P = 10,000, R = 5% and t = 2 years. This gives A = 10,000 × (1.05)². The square of 1.05 is 1.1025, so the amount becomes 10,000 × 1.1025 = ₹11,025. This includes both the original principal and the interest earned over two years.

Option A:
Option A, ₹10,500, represents the amount after one year of compound or simple interest at 5%, not two years. It misses the second period of compounding.

Option B:
Option B, ₹11,000, may come from incorrectly adding 5% of 10,000 twice and ignoring the interest on interest, which is the essence of compounding.

Option C:
Option C, ₹11,250, overestimates the effect of compounding and does not match the precise factor (1.05)². It might arise from using an incorrect growth factor.

Option D:
Option D uses the exact compounding formula and incorporates the second year’s interest on the first year’s interest. It therefore gives the correct accumulated amount of ₹11,025.

Statements A, B, D and E are correct. A restates the basic simple interest rule. B is true because with annual compounding, one compounding per year means effective and nominal rates coincide. D is correct since more frequent compounding at the same nominal rate increases total interest. E is also true; at low rates and short durations, simple and compound interest often differ negligibly. C is false because more frequent compounding makes the effective annual rate higher, not lower, than the nominal rate. So A, B, D and E only are correct.

Option A:
Option A is incomplete because it omits E, which notes the practical observation that, for small rates and short periods, the difference between SI and CI can be very small.

Option B:
Option B is correct since it collects all the accurate statements about calculation bases, effective rates and compounding frequency, while excluding C, which reverses the relationship between nominal and effective rates.

Option C:
Option C is wrong because it includes C, which misstates the effect of multiple compounding periods, and therefore cannot represent the full set of correct statements.

Option D:
Option D is incorrect as it retains C (false) and omits B (true), so it both includes an error and misses a key correct statement.

A, B and D correctly explain fundamental ideas about simple and compound interest. Simple interest remains based on the original principal, compound interest periodically adds interest to principal to generate interest-on-interest, and increasing compounding frequency (for the same nominal rate and duration) increases the final amount. Statement C is wrong because compound interest for the same principal, rate and time is greater than or equal to simple interest, not less, and E is wrong because rate and time are central factors in every interest formula. Hence the set A, B and D only is the correct combination of true statements.

Option A:
Option A includes A and B but omits D, thereby ignoring the important effect of compounding frequency on the final amount. Although it contains two true statements, the absence of D means it does not cover all correct information listed.

Option B:
Option B selects B and D but leaves out A, failing to mention the defining feature of simple interest, namely that it is calculated only on the original principal. Without A, understanding of the contrast between simple and compound interest is incomplete.

Option C:
Option C is incorrect because it includes E, which wrongly claims that rate and time are irrelevant, and excludes B, one of the key statements about compound interest. The presence of a clearly false statement makes this option invalid.

Option D:
Option D is correct since it groups the three true statements that cover simple interest behaviour, the nature of compounding and the effect of compounding frequency, while excluding C and E, both of which misrepresent interest calculations.