A certain sum is deposited in a bank which gives compound intrest at certain rate. The intrest on the amount is rs.440. In the first 2 years and rs.728 in the first 3 years what is the rate of interest per annum.
To find the rate of interest per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial amount deposited)
r = rate of interest (in decimal form)
n = number of times interest is compounded per year
t = number of years
Let's use the given information to solve for the rate of interest.
From the question, we know that the interest earned in the first 2 years is Rs. 440. This means the final amount after 2 years is P + 440.
A = P + 440
In the second scenario, the interest earned in the first 3 years is Rs. 728. This means the final amount after 3 years is P + 728.
A = P + 728
Using these two equations, we can set up a system of equations to solve for the rate of interest.
Equation 1: A = P + 440
Equation 2: A = P + 728
Since both equations are equal to A, we can set them equal to each other:
P + 440 = P + 728
Subtracting P from both sides:
440 = 728
This doesn't make sense, as both sides of the equation are not equal. There might be an error in the given information or in the equations provided. Please check the values and equations again before proceeding.
x((1+r)^2-1) = 440
x((1+r)^3-1) = 728
((1+r)^3-1)/((1+r)^2-1) = 728/440
r = 1/5 = 0.2 = 20%