Answer
Rate of Interest = 20%
Work Step by Step
Amount (A) = 2880
Principal (P) = 2000
Time (t) = 2
We have to find the rate of interest i.e. r.
Step-1: Substitute the given values in the formula.
$A=P(1+r)^t$
$2880=2000 (1+r)^2$
Step-2: We now solve the equation for r.
$2880=2000 (1+r)^2$
Step-3: Divide both sides of the equation by 2000
$\frac{2880}{2000}=(1+r)^2$
Step-4: Use the square root property
$±\sqrt\frac{2880}{2000}=1+r$
Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 2880 and 2000
H.C.F of 2880 and 2000 is 80
$±\sqrt\frac{2880\div80}{2000\div80}=1+r$
$±\sqrt\frac{36}{25}=1+r$
$±\frac{6}{5}=1+r$
Step-6: Subtract both the sides with 1 and further simplify the left hand side
$±\frac{6}{5}−1=r$
$\frac{±6-5}{5}=r$
Therefore,$ r=\frac{1}{5},\frac{−11}{5}$
Rate of Interest cannot be negative, hence, $r=\frac{1}{5}=0.2=$20%
