At what percent rate vompound interest isRs 700 amount to Rs 847 in 2 year?

To calculate the compound interest rate, we need to use the formula:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

Given:
A = Rs 847
P = principal amount
r = compound interest rate
n = number of times interest is compounded per year (assuming it is compounded annually)
t = 3 years

We need to solve for r:

847 = P(1 + r/1)^(1*3)
847 = P(1 + r)^3

Since we do not have the principal amount, we cannot calculate the exact compound interest rate.

Let the rate of interest be r% per annum. Then,

$$847 = 100P[ (1 + \frac{r}{100})^3 - 1 ]$$

$$847 = 100P [ \frac{(100+r)^3 - 100^3}{100^3} ]$$

$$847 = 100P [ \frac{3r^2 + 300r }{100^3} ]$$

$$847 = 100P [\frac{r^2 + 100r }{100^2}]$$

$$847 = P ( r^2 + 100r )$$

$$r^2 + 100r - 847 = 0$$

$$( r - 7 )( r + 121 ) = 0$$

$$r = 7, -121$$

The rate of interest cannot be negative. Therefore, r = 7.

Hence, the rate of interest is 7% per annum.