At a certain rate of interest per annum compounded annually a certain sum of money amounts to two ti...........

Quantitative Aptitude (MTS) Compound Interest

At a certain rate of interest per annum, compounded annually, a certain sum of money amounts to two times of itself in 11

years. In how many years will the sum of money amount to four times of itself at the previous rate of interest per annum, also

compounded annually?

This questions was previously asked in

SSC MTS 22nd July 2022 Shift-1

20 years

5.5 years

22 years

33 years

- We need to determine how many years it takes for the sum to quadruple when it doubles in 11 years at the same interest rate.

- Given, the sum doubles in 11 years: \(2P = P(1 + r)^{11}\), yields \( (1 + r)^{11} = 2 \).

- Now, we are looking when the sum becomes four times: \(4P = P(1 + r)^n\), so \( (1 + r)^n = 4 \).

- Since \( (1 + r)^{11} = 2 \), if squaring both sides, \( (1 + r)^{22} = 4 \).

- Therefore, the sum will quadruple in 22 years.

- Correct Option: 3, 22 years.

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