The compound interest on a certain sum for 2 years is Rs 41 and simple interest is Rs 40.Then the rate per annum is
20
To find the rate per annum, we can use the formulas for compound interest and simple interest.
Compound interest is calculated using the formula:
A = P (1 + r/n)^(n*t)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount (the initial amount)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
Simple interest is calculated using the formula:
A = P + (P * r * t)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount (the initial amount)
r = annual interest rate (in decimal form)
t = number of years
Given that the compound interest is Rs 41 and the simple interest is Rs 40 for 2 years, we can set up the equations:
P (1 + r/n)^(n*t) = P + (P * r * t)
Let's assume the principal amount P is Rs X.
For the compound interest:
X (1 + r/n)^(n*t) = X + (X * r * t)
X (1 + r/n)^(n*2) = X + (X * r * 2)
For the simple interest:
X + (X * r * 2) = X + 40
Now, we need to solve these two equations to find the rate per annum (r). We can simplify the equations as follows:
Equation 1:
X (1 + r/n)^(n*2) = X + (X * r * 2)
Divide both sides by X:
(1 + r/n)^(n*2) = 1 + r*2
Equation 2:
X*r*2 = 40
Divide both sides by X*2:
r = 20/X
Now, substitute r = 20/X in Equation 1:
(1 + 20/(X*n))^2n = 1 + 20
To solve for the rate per annum (r), we need to assign a value to the principal amount (X) and find the value of n that satisfies the equation. Unfortunately, without additional information, it is not possible to determine the exact value of the rate per annum.