2420=2000(1+r)2

Rewrite the equation as 2000(1+r)2=2420.

2000(1+r)2=2420

Divide each term in 2000(1+r)2=2420 by 2000.

2000(1+r)22000=24202000

Cancel the common factor of 2000.

Cancel the common factor.

2000(1+r)22000=24202000

Divide (1+r)2 by 1.

(1+r)2=24202000

(1+r)2=24202000

Cancel the common factor of 2420 and 2000.

Factor 20 out of 2420.

(1+r)2=20(121)2000

Cancel the common factors.

Factor 20 out of 2000.

(1+r)2=20⋅12120⋅100

Cancel the common factor.

(1+r)2=20⋅12120⋅100

Rewrite the expression.

(1+r)2=121100

(1+r)2=121100

(1+r)2=121100

(1+r)2=121100

Take the square root of each side of the equation to set up the solution for r

(1+r)2⋅12=±121100

Remove the perfect root factor 1+r under the radical to solve for r.

1+r=±121100

Rewrite 121100 as 121100.

1+r=±121100

Simplify the numerator.

Rewrite 121 as 112.

1+r=±112100

Pull terms out from under the radical, assuming positive real numbers.

1+r=±11100

1+r=±11100

Simplify the denominator.

Rewrite 100 as 102.

1+r=±11102

Pull terms out from under the radical, assuming positive real numbers.

1+r=±1110

1+r=±1110

1+r=±1110

First, use the positive value of the ± to find the first solution.

1+r=1110

Move all terms not containing r to the right side of the equation.

Subtract 1 from both sides of the equation.

r=1110-1

To write -1 as a fraction with a common denominator, multiply by 1010.

r=1110-1⋅1010

Combine -1 and 1010.

r=1110+-1⋅1010

Combine the numerators over the common denominator.

r=11-1⋅1010

Simplify the numerator.

Multiply -1 by 10.

r=11-1010

Subtract 10 from 11.

r=110

r=110

r=110

Next, use the negative value of the ± to find the second solution.

1+r=-1110

Move all terms not containing r to the right side of the equation.

Subtract 1 from both sides of the equation.

r=-1110-1

To write -1 as a fraction with a common denominator, multiply by 1010.

r=-1110-1⋅1010

Combine -1 and 1010.

r=-1110+-1⋅1010

Combine the numerators over the common denominator.

r=-11-1⋅1010

Simplify the numerator.

Multiply -1 by 10.

r=-11-1010

Subtract 10 from -11.

r=-2110

r=-2110

Move the negative in front of the fraction.

r=-2110

r=-2110

The complete solution is the result of both the positive and negative portions of the solution.

r=110,-2110

r=110,-2110

Solve Using the Square Root Property 2420=2000(1+r)^2