Apologies for being rusty..
I was recently looking at the calculation of yield to maturity for bonds and was wondering why people in the industry resort to a trial error approach when calculating them.
The YTM calculations boil down to equations like these, where i is the YTM
(Source: https://www.investopedia.com/terms/y/yieldtomaturity.asp):
So my specific question is
1) Can the above equation be re-arranged to a form
i = ...where I can calculate the right side numerically?
and my general question would be
2) Can't all equations with a single unknown be transformed into
i = ...?
You can note that $(1+i)$ is to the power 5. In the complex world, there are 5 solutions to the equation $(1+x)^5 = a$. If you are dealing with positive reals (assuming i is a positive reals), there is only one solution (sometimes none). So we will assume that $i$ is a positive or zero real.
1) is no in the complex world. However there are techniques to solve it using computers.
2) is no.