7250=5100(1+R)120

Rewrite the equation as 5100(1+R)120=7250.

5100(1+R)120=7250

Divide each term in 5100(1+R)120=7250 by 5100.

5100(1+R)1205100=72505100

Cancel the common factor of 5100.

Cancel the common factor.

5100(1+R)1205100=72505100

Divide (1+R)120 by 1.

(1+R)120=72505100

(1+R)120=72505100

Cancel the common factor of 7250 and 5100.

Factor 50 out of 7250.

(1+R)120=50(145)5100

Cancel the common factors.

Factor 50 out of 5100.

(1+R)120=50⋅14550⋅102

Cancel the common factor.

(1+R)120=50⋅14550⋅102

Rewrite the expression.

(1+R)120=145102

(1+R)120=145102

(1+R)120=145102

(1+R)120=145102

Take the 120th root of each side of the equation to set up the solution for R

(1+R)120⋅1120=±145102120

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

1+R=±145102120

Rewrite 145102120 as 145120102120.

1+R=±145120102120

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

1+R=145120102120

Subtract 1 from both sides of the equation.

R=145120102120-1

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

1+R=-145120102120

Subtract 1 from both sides of the equation.

R=-145120102120-1

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

R=145120102120-1,-145120102120-1

R=145120102120-1,-145120102120-1

The result can be shown in multiple forms.

Exact Form:

R=145120102120-1,-145120102120-1

Decimal Form:

R=0.00293564…,-2.00293564…

Solve for R 7250=5100(1+R)^120