the sum of money will amount to rupees 12000 in 2 years at the rate of 10% per annum compounded anually
x(1.1)^2 = 12000
x = 12000/1.1^2 = appr 9917.36
To calculate the compound interest for this scenario, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = principal amount (initial sum of money)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = unknown
A = 12,000 rupees
r = 10% per annum (or 0.10)
n = 1 (compounded annually)
t = 2 years
Substituting the given values into the formula, we get:
12,000 = P(1 + 0.10/1)^(1*2)
Simplifying the equation:
12,000 = P(1 + 0.10)^2
Expanding the equation:
12,000 = P(1.10)^2
Calculating the exponent:
12,000 = 1.21P
Now, we can solve for P by dividing both sides of the equation by 1.21:
P = 12,000 / 1.21
P ≈ 9,917.35 rupees
Therefore, the principal amount (initial sum of money) is approximately 9,917.35 rupees.