The difference between the simple interest and compound interest on a certain sum for 2 years at the rate of 5% per annum is rupees 205.find the sum.
let the sum be x
x(1.05)^2 - x - x(.05)(2) = 205
x(1.05^2 - 1 - .05(2) ) = 205
....
let me know what you got
To find the sum, we need to calculate the difference between the simple interest and compound interest. Here is how you can solve the problem:
1. Calculate the simple interest using the formula:
Simple Interest = (Principal * Rate * Time) / 100
Let's assume the principal sum is P. The simple interest for 2 years at a rate of 5% can be calculated as:
Simple Interest = (P * 5 * 2) / 100 = (10P / 100) = P / 10
2. Calculate the compound interest using the formula:
Compound Interest = P * (1 + Rate/100)^Time - P
For 2 years at a rate of 5%, the formula becomes:
Compound Interest = P * (1 + 5/100)^2 - P
= P * (21/20)^2 - P
= P * (441/400) - P
= P * (441 - 400) / 400
= 41P / 400
3. Find the difference between the compound interest and simple interest:
Difference = Compound Interest - Simple Interest
= (41P / 400) - (P / 10)
= P*(41/400 - 1/10)
= P*(41/400 - 40/400)
= P*(1/400)
= P / 400
Given that the difference is Rs. 205, we can set up the equation:
P / 400 = 205
To solve for P, multiply both sides by 400:
P = 205 * 400
P = 82000
Therefore, the sum (principal) is Rs. 82000.