A principal becomes 25 times, in how many years if the interest is being compounded yearly? Statement I: A sum becomes 9 times in a year when interest is being compounded half yearly. Statement II: The principal amount is 34500. Statement III: In half yearly calculation the rate of interest will become half and the time will be double.

Statement I: sum becomes 9 times in 1 year with half-yearly compounding. Half-yearly means 2 periods. If rate=r% per half-year, then P(1+r)²=9P, so (1+r)²=9, 1+r=3, r=200%. Annual rate=400%. For principal to become 25 times annually: P(1+4)ⁿ=25P, so 5ⁿ=25, n=2 years. Statement II gives principal amount which is irrelevant. Statement III states formula for half-yearly compounding (standard knowledge). Only Statement I is needed.