66200=20000((1 + R)^3 - 1) / R), solve for R
Solve for R:
66200 = (20000 ((R+1)^3-1))/R
66200 = (20000 ((R+1)^3-1))/R is equivalent to (20000 ((R+1)^3-1))/R = 66200:
(20000 ((R+1)^3-1))/R = 66200
Multiply both sides by R:
20000 ((R+1)^3-1) = 66200 R
Expand out terms of the left hand side:
20000 R^3+60000 R^2+60000 R = 66200 R
Subtract 66200 R from both sides:
20000 R^3+60000 R^2-6200 R = 0
The left hand side factors into a product with four terms:
200 R (10 R-1) (10 R+31) = 0
Divide both sides by 200:
R (10 R-1) (10 R+31) = 0
Split into three equations:
R = 0 or 10 R-1 = 0 or 10 R+31 = 0
Add 1 to both sides:
R = 0 or 10 R = 1 or 10 R+31 = 0
Divide both sides by 10:
R = 0 or R = 1/10 or 10 R+31 = 0
Subtract 31 from both sides:
R = 0 or R = 1/10 or 10 R = -31
Divide both sides by 10:
R = 0 or R = 1/10 or R = -31/10
(20000 ((R+1)^3-1))/R => -(20000 ((1-31/10)^3-1))/(31/10) = 66200:
So this solution is correct
(20000 ((R+1)^3-1))/R => 20000/0 ((1+0)^3-1) = (undefined):
So this solution is incorrect
(20000 ((R+1)^3-1))/R => (20000 ((1+1/10)^3-1))/(1/10) = 66200:
So this solution is correct
The solutions are:
Answer: | R = 1/10 or R = -31/10 R=1/10 x 100 =10%