Final answer:
To determine the time, the compound interest formula is applied to the given principal and interest amounts. By substituting the values and solving for t, it's found that the time needed to yield a compound interest of Rs. 477 from Rs. 1875 at 12% compounded annually is approximately 2 years. Therefore correct option is A
Step-by-step explanation:
The question asks in what time the sum of Rs. 1875 will yield a compound interest of Rs. 477 at a rate of 12% per annum when compounded annually.
To find the time, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount after time t, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Given that the interest earned is Rs. 477, the final amount A is Rs. 1875 + 477 = Rs. 2352.
Using the formula and the given interest rate of 12%, we can solve for t:
2352 = 1875(1 + 0.12/1)^(1*t) → 2352
= 1875 * (1.12)^t
By dividing both sides by 1875 and taking the logarithm to solve for t, we find:
t = log(2352/1875) / log(1.12)
Upon calculation, it's approximately t = 2 years, which means the correct answer is Option A. 2 years