Answer: Option B
Given, Principal amount (P) = ?Amount after 2 years (A2) = Rs. 14,520Amount after 3 years (A3) = Rs. 15,972Rate of interest (r) = ?Time (n) = ?
As we know, the formula to calculate compound interest is:A = P (1 + r/n)^(n*t)
where,A = AmountP = Principal amountr = Rate of interestn = Number of times interest is compounded in a yeart = Time
Since the interest is compounded annually, we can assume that n = 1
Using the above formula, we can form two equations based on the given information:
Equation 1: 14,520 = P (1 + r/1)^(12)Equation 2: 15,972 = P (1 + r/1)^(13)
We can solve these equations to find the value of r.
Dividing equation 2 by equation 1, we get:
15,972/14,520 = (1 + r)^1/(1 + r)^21.1013 = 1/(1 + r)
Taking the reciprocal of both sides, we get:
1/(1.1013) = 1 + rr = 0.0916 or 9.16%
Therefore, the rate of interest is 9.16%. However, this is the annual rate of interest. The question asks for the rate of interest per annum. We can convert the annual rate of interest to per annum rate by using the formula:
Per annum rate = (1 + Annual rate/n)^n - 1
where n is the number of times the interest is compounded in a year.
In this case, n = 1 (since the interest is compounded annually)
Per annum rate = (1 + 0.0916/1)^1 - 1= 0.10 or 10%
Hence, the correct answer is option B (10%).If you think the solution is wrong then please provide your own solution below in the comments section .