Solve for r 535.29=400(1+r)^5

$535.29 = 400 {(1 + r)}^{5}$

Rewrite the equation as $400 {(1 + r)}^{5} = 535.29$ .

$400 {(1 + r)}^{5} = 535.29$

Divide each term in $400 {(1 + r)}^{5} = 535.29$ by $400$ and simplify.

Divide each term in $400 {(1 + r)}^{5} = 535.29$ by $400$ .

$\frac{400 {(1 + r)}^{5}}{400} = \frac{535.29}{400}$

Simplify the left side.

Cancel the common factor of $400$ .

Cancel the common factor.

$\frac{400 {(1 + r)}^{5}}{400} = \frac{535.29}{400}$

Divide ${(1 + r)}^{5}$ by $1$ .

${(1 + r)}^{5} = \frac{535.29}{400}$

Simplify the right side.

Divide $535.29$ by $400$ .

${(1 + r)}^{5} = 1.338225$

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

$1 + r = \sqrt[5]{1.338225}$

Subtract $1$ from both sides of the equation.

$r = \sqrt[5]{1.338225} - 1$

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt[5]{1.338225} - 1$

Decimal Form:

$r = 0.05999990 \dots$