Question

410 = 4000 ( 1+ r/100 )2

Answer 1

Let's solve your equation step-by-step.

$410=4000(1+\frac{r}{100})2$

Step 1: Simplify both sides of the equation.

$410=4000(1+\frac{r}{100})(2)$

(Distribute)

$410=80r+8000$

Step 2: Flip the equation.

$80r+8000=410$

Step 3: Subtract 8000 from both sides.

$80r+8000-8000=410-8000$

$80r=-7590$

Step 4: Divide both sides by 80.

$\frac{80r}{80} =\frac{-7590}{80}$

$r=\frac{-759}{8}$

Verification

Now, we have to verify if $r=\frac{-759}{8}$ in the equation ⇒ $410=4000(1+\frac{r}{100})2$

⇒ $410=4000(1+\frac{r}{100})2$

⇒ $410=4000(1+\frac{\frac{-759}{8} }{100})2$

⇒ $4000(1+\frac{{-759} }{800})2$

⇒ $4000(\frac{41}{800})(2)$

⇒ $(205)(2)$

⇒ $410$

∴  $r=\frac{-759}{8}$ in the equation ⇒ $410=4000(1+\frac{r}{100})2$

Answer 2

Simplify Right Sides
410 = 8000 + 80r


Swap sides
8000 + 80r = 401


Subtract from both sides
(8000+80r) - 8000 = 410 - 8000


Simply Left side
80r = 410 - 8000


Simplify Arithmetic
80r = - 7590


$\sf \: Divide \: from \: Both \: sides \\ \sf \: \frac{80r}{80} = - \frac{7590}{80} \\ \\ \\ \sf \: Simplify \: Fraction \\ \sf \: r = \frac{7590}{80} \\ \\ \\ \sf \: Simplify \: Fraction \\ \sf \: r = \frac{759}{8} \\ \\ \\ \boxed{ \sf r = 94.875}$