#### Answer

Rate of interest r = 11.11%

#### Work Step by Step

Amount (A) = 1000
Principal (P) = 810
Time (t) = 2
We have to find the rate of interest i.e. r.
Step-1: Substitute the given values in the formula.
$A=P(1+r)^t$
$1000=810 (1+r)^2$
Step-2: We now solve the equation for r.
$1000=810 (1+r)^2$
Step-3: Divide both sides of the equation by 800
$\frac{1000}{810}=(1+r)^2$
Step-4: Use the square root property
$±\sqrt\frac{1000}{810}=1+r$
Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 1000 and 810
H.C.F of 1000 and 810 is 10
$±\sqrt\frac{1000\div10}{810\div10}=1+r$
$±\sqrt\frac{100}{81}=1+r$
$±\frac{10}{9}=1+r$
Step-6: Subtract both the sides with 1 and further simplify the left hand side
$±\frac{10}{9}−1=r$
$\frac{±10-9}{9}=r$
Therefore, $ r=\frac{1}{9},\frac{−19}{9}$
Rate of Interest cannot be negative, hence, $r=\frac{1}{9}=0.1111=$11.11%.