Answer
Interest rate is 5%
Work Step by Step
Given:
Amount (A) = 1764
Principal (P) = 1600
Time (t) = 2
We have to find the rate of interest i.e. $r$
Step-1: Substitute the given values in the formula
$A=P(1+r)^t$
$1764=1600(1+r)^2$
Step-2: We now solve the equation for $r$
$1764=1600(1+r)^2$
Step-3: Divide both sides of the equation by $1600$
$\frac{1764}{1600}=(1+r)^2$
Step-4: Use the square root property
$±\sqrt (\frac{1764}{1600})=1+r$
$±\frac{42}{40}=1+r$
Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 42 and 40
H.C.F of 42 and 40 is 2
$±\frac{42\div2}{40\div2}=1+r$
$±\frac{21}{20}=1+r$
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, $r = \frac{1}{20} = 0.05 = 5$%
