Compound Interest Rate Calculation

Let the principal amount be $P$ and the annual compound interest rate be $r$. The formula for the amount $A$ after $t$ years is given by $A = P(1 + r)^t$.

Given Information

• Amount after 2 years: $A_2 = ₹6,400$
• Amount after 4 years: $A_4 = ₹8,100$

Applying the Formula

From the given information, we can write two equations:

1. $6400 = P(1 + r)^2$
2. $8100 = P(1 + r)^4$

Finding the Rate

To find the rate $r$, divide the second equation by the first equation:

$ \frac{8100}{6400} = \frac{P(1 + r)^4}{P(1 + r)^2} $

Simplify the equation:

$ \frac{81}{64} = (1 + r)^{4-2} $

$ \frac{81}{64} = (1 + r)^2 $

Take the square root of both sides:

$ \sqrt{\frac{81}{64}} = 1 + r $

$ \frac{9}{8} = 1 + r $

Solving for r

Now, solve for $r$:

$ r = \frac{9}{8} - 1 $

$ r = \frac{9 - 8}{8} $

$ r = \frac{1}{8} $

Convert the rate to a percentage:

$ r = \frac{1}{8} \times 100\% $

$ r = 12.5\% $

The rate of compound interest is $12.5\%$.