If a certain principal of Rs.256 will become Rs. 289 in two years. Then, find the rate ofcompound inte

Sure, here is the step by step solution:

Step 1: Understand the problem The problem is asking to find the rate of compound interest. We know the principal amount (Rs. 256), the amount after two years (Rs. 289), and the time period (2 years).

Step 2: Use the formula for compound interest The formula for compound interest is A = P(1 + r/n)^(nt), where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, we are trying to find r (the annual interest rate), so we need to rearrange the formula to solve for r.

Step 3: Substitute the given values into the formula 289 = 256(1 + r/1)^(1*2)

Step 4: Solve for r First, divide both sides of the equation by 256 to get: 1.12890625 = (1 + r)^2

Then, take the square root of both sides to get: 1.064492753 = 1 + r

Finally, subtract 1 from both sides to get: 0.064492753 = r

Step 5: Convert r to a percentage To convert r to a percentage, multiply by 100: 6.4492753% = r

So, the rate of compound interest is approximately 6.45%.