#### Answer

Rate of interest is r = 5%

#### Work Step by Step

Amount (A) = 882
Principal (P) = 800
Time (t) = 2
We have to find the rate of interest i.e. r.
Step-1: Substitute the given values in the formula.
$A=P(1+r)^t$
$882=800 (1+r)^2$
Step-2: We now solve the equation for r.
$882=800 (1+r)^2$
Step-3: Divide both sides of the equation by 800
$\frac{882}{800}=(1+r)^2$
Step-4: Use the square root property
$±\sqrt\frac{882}{800}=1+r$
Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 882 and 800
H.C.F of 882 and 800 is 2
$±\sqrt\frac{882\div2}{800\div2}=1+r$
$±\sqrt\frac{441}{400}=1+r$
$±\frac{21}{20}=1+r$
Step-6: Subtract both the sides with 1 and further simplify the left hand side
$±\frac{21}{20}−1=r$
$±\frac{21-20}{20}=r$
Therefore,$ r=\frac{1}{20},\frac{−41}{20}$
Rate of Interest cannot be negative, hence, $r=\frac{1}{20}=0.05=$5%.