How to calculate the yield to maturity?

Question

I am looking at an example problem in my textbook and its solution. Can someone look at this picture/ problem and its solution and tell me where they got the yield to maturity.

Answer 1

The yield maturity is the constant discount rate that makes the present value of the cash flows equal to the bond price.

Thus

$$114.49 = 100(1+y)^{-4} + 10\sum_{k=1}^{4} (1+y)^{-k} = 10\frac{(1+y)^{-1}[1-(1+y)^{-4}]}{1 - (1+y)^{-1}}+100(1+y)^{-4}\\=10\frac{1-(1+y)^{-4}}{y}+100(1+y)^{-4}$$

Solving numerically (using for example Newton's method) we find $y= 0.05834= 5.834\, \%.%$