Answer:
Rs. 20827.
Explanation:
Let's denote the principal amount as P and the annual interest rate as r. Since interest is compounded semi-annually, the interest rate per compounding period is r/2 and the number of compounding periods in 1 year and 2 years are 2 and 4, respectively.
Using the formula for compound interest, we can write:
P(1 + r/2)^2 - P = 2100 (1)
P(1 + r/2)^4 - P = 4641 (2)
Simplifying equation (1), we get:
P[(1 + r/2)^2 - 1] = 2100
P(r + 2)/(100*2) = 2100
Simplifying equation (2), we get:
P[(1 + r/2)^4 - 1] = 4641
P(r + 2)/(100*2) * [(1 + r/2)^2 + 1] = 4641
Dividing equation (2) by equation (1), we get:
[(1 + r/2)^2 + 1]/2 = 4641/2100
(1 + r/2)^2 + 1 = 4641/1050
(1 + r/2)^2 = (4641/1050) - 1
Taking the square root of both sides, we get:
1 + r/2 = sqrt[(4641/1050) - 1]
r/2 = sqrt[(4641/1050) - 1] - 1
r = 2 * [sqrt((4641/1050) - 1) - 1]
Using equation (1) to solve for P, we get:
P = 2100 / [(1 + r/2)^2 - 1]
Substituting the value of r into the above equation, we get:
P = 2100 / [(1 + 2 * [sqrt((4641/1050) - 1) - 1]/2)^2 - 1]
Simplifying, we get:
P = 42000 / (23 + 16 * sqrt((4641/1050) - 1))
Therefore, the rate of interest is approximately 10.14% and the principal amount is approximately Rs. 20827.