Final answer:
To solve for the initial amount with compound interest, we would need the starting interest rate and the compounding period, which are not provided in the question. Therefore, it is not possible to calculate the initial amount and select the right option without further information.
Step-by-step explanation:
The question pertains to computing the initial amount of money given a specific annual cyclical interest rate and the final amount of interest accrued. With an interest rate increasing by 0.10 every 6 months, we understand that the interest is indeed compound interest, not simple, since it changes periodically. Now, since the annual cyclical interest turns Rs.4000 into Rs.1324 over some time, we can deduce that Rs.1324 is the interest earned over one complete year on the principal amount.
However, with the information at hand, it isn't sufficient to determine the starting principal since we need to know the original interest rate or the number of cycles/periods it took to achieve the said interest. We may have to apply the compound interest formula, A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
Without the missing data (initial interest rate or time), we can't provide a numerical answer, and thus none of the problem's answer choices (A, B, C, D) can be identified as correct with complete confidence using the provided information.