1000=186.29*((1+r)^4-1)/r solve for r

asked by guest
on Jan 15, 2025 at 9:35 am



You asked:

Solve the equation \[1000 = \frac{186.29 \left({\left( 1 + r \right)}^{4} - 1\right)}{r}\] for the unknown \(r\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}r &= - \frac{4}{3} + \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}} - \frac{2}{9 \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}}} \approx 0.19999672\\r &= - \frac{4}{3} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}} - \frac{2}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}}} \approx -2.0999984 -1.5588433 i\\r &= - \frac{4}{3} - \frac{2}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1163710}{502983} + \frac{2 \sqrt{37694368923}}{167661}} \approx -2.0999984 + 1.5588433 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

+ Submit Question