The difference between the compound interest and simple interest on a certain sum for 2 years at 6 % per annum is rs. 90. Find the sum.
let the amount be x
x(1.06)^2 - x(1 + 2(.06)) = 92
x(1.1236) - x(1.12) = 92
.0036x = 92
x =25,555.56
To find the sum, we need to use the formula for compound interest and simple interest.
Compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = Total amount after time t
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Simple interest formula:
A = P(1 + r*t)
Where:
A = Total amount after time t
P = Principal amount
r = Annual interest rate (as a decimal)
t = Number of years
First, let's assume the principal amount is x.
Using the compound interest formula, the total amount after 2 years would be:
A = x(1 + 0.06/1)^(1*2)
A = x(1 + 0.06)^2
A = 1.1236x
Using the simple interest formula, the total amount after 2 years would be:
A = x(1 + 0.06*2)
A = x(1 + 0.12)
A = 1.12x
Given that the difference between the compound interest and simple interest is Rs. 90, we can set up the following equation:
1.1236x - 1.12x = 90
Simplifying the equation:
0.0036x = 90
To find the value of x, divide both sides of the equation by 0.0036:
x = 90 / 0.0036
x = 25000
Therefore, the principal amount (sum) is Rs. 25,000.