Finite Math Examples

$5000 = 4000 {(1 + r)}^{365}$

Step 1

Rewrite the equation as $4000 {(1 + r)}^{365} = 5000$ .

$4000 {(1 + r)}^{365} = 5000$

Step 2

Divide each term in $4000 {(1 + r)}^{365} = 5000$ by $4000$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $4000 {(1 + r)}^{365} = 5000$ by $4000$ .

$\frac{4000 {(1 + r)}^{365}}{4000} = \frac{5000}{4000}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $4000$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{4000 {(1 + r)}^{365}}{4000} = \frac{5000}{4000}$

Step 2.2.1.2

Divide ${(1 + r)}^{365}$ by $1$ .

${(1 + r)}^{365} = \frac{5000}{4000}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $5000$ and $4000$ .

Tap for more steps...

Step 2.3.1.1

Factor $1000$ out of $5000$ .

${(1 + r)}^{365} = \frac{1000 (5)}{4000}$

Step 2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.2.1

Factor $1000$ out of $4000$ .

${(1 + r)}^{365} = \frac{1000 \cdot 5}{1000 \cdot 4}$

Step 2.3.1.2.2

Cancel the common factor.

${(1 + r)}^{365} = \frac{1000 \cdot 5}{1000 \cdot 4}$

Step 2.3.1.2.3

Rewrite the expression.

${(1 + r)}^{365} = \frac{5}{4}$

Step 3

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

$1 + r = \sqrt[365]{\frac{5}{4}}$

Step 4

Rewrite $\sqrt[365]{\frac{5}{4}}$ as $\frac{\sqrt[365]{5}}{\sqrt[365]{4}}$ .

$1 + r = \frac{\sqrt[365]{5}}{\sqrt[365]{4}}$

Step 5

Subtract $1$ from both sides of the equation.

$r = \frac{\sqrt[365]{5}}{\sqrt[365]{4}} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\sqrt[365]{5}}{\sqrt[365]{4}} - 1$

Decimal Form:

$r = 0.00061153 \dots$