Since is on the right side of the equation, switch the sides so it is on the left side of the equation.

Multiply both sides of the equation by .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Add to both sides of the equation.

Add and .

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

Expand by moving outside the logarithm.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x 5000=(100((1.01)^n-1))/0.01