Find r if 0.106508=(1+(r/4))^4-1

Question

I need to know the answer with the steps 

Answer 1

Starting with:

0.106508=(1+(r/4))^4-1

add 1 to both sides:

1.106508=(1+(r/4))^4

take the fourth root of both sides:

1.106508^(1/4) = 1+(r/4)

1.025625 = 1+r/4

0.025625 = r/4

0.1025 = r

or

10.25% = r

 

Answer 2

Just like any process, take it one step at a time. Since we have to isolate r, which is in two sets of parentheses, we need to work to remove the parentheses from around r.

First, add 1 to both sides

1 + 0.106508 = (1 + (r/4))⁴

Now we need to get rid of the exponent, so we need to take the fourth root of both sides

⁴√(1.106508) = ⁴√(1 + (r/4))⁴  ===> 1.025625 = (1 + r/4)

Subtract one from both sides to get

0.025625 =  r/4

Multiply each side by 4 to isolate r

4(.025625) = (4) (r/4)

0.1025 = r

Answer 3

0.106508 = (1 + r/4)⁴ - 1                      Given

0.106508 + 1 = (1 + r/4)⁴ - 1 + 1           Add 1 to both sides

1.106508 = (1 + r/4)⁴                           Simplify

+/- ⁴√1.106508 = 1 + r/4                      Take the fourth root of each side

+/- ⁴√1.106508 -1 = 1 + r/4 -1              Subtract 1 from each side

-1 +/- ⁴√1.106508 = r/4                       Simplify

4(-1 +/- ⁴√1.106508) = 4(r/4)              Multiply both sides by 4

r = -4 +/- 4(⁴√1.106508)                      Distribute the 4 and simplify