UPSC Prelims 2023 · CSAT
Question 44: Basic Numeracy
A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct ?
AnswerUPSC’s answer is (c).
The same P becomes the same Q in one year under both schemes. Half-yearly compounding at R% gives P(1 + R/200)^2 = P(1 + R/100 + R^2/40000). Annual compounding at S% gives P(1 + S/100). Equating the two, S = R + R^2/400, which is greater than R. Interest is earned on interest sooner under half-yearly compounding, so a lower rate reaches the same amount: R < S.
Why each option is right or wrong
- (a) Wrong: equal rates would give more under half-yearly compounding.
- (b) Wrong: a higher R would give a larger amount than annual compounding.
- (c) Right: S = R + R^2/400 > R.
- (d) Wrong: equality is impossible for a positive rate.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.