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?

Question

Accepted Answer

The correct answer is option C. For half-yearly compounding, the amount Q after 1 year is given by Q = P * (1 + (R/2)/100)^(1*2) = P * (1 + R/200)^2.
For annual compounding, the amount Q after 1 year is given by Q = P * (1 + S/100)^1.
Since the final amount Q is the same in both cases:
P * (1 + R/200)^2 = P * (1 + S/100)
(1 + R/200)^2 = 1 + S/100
Expanding the left side: 1 + 2*(R/200) + (R/200)^2 = 1 + S/100
1 + R/100 + R^2/40000 = 1 + S/100
Subtracting 1 from both sides and multiplying by 100:
R + R^2/400 = S
Since R is an annual rate of interest, R must be positive. Therefore, R^2/400 will be a positive value. This means S is equal to R plus a positive quantity. Hence, S > R, or R < S.

Q74. 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?

Detailed Solution

More Basic Numeracy Questions

More from UPSC 2023 CSAT

Ace UPSC with AI-powered Practice