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Is there a simple/fast way to find $y$ for the equation:

$$120,000=8000\sum_{t=1}^{4}\frac{1}{(1+y)^t}+\frac{100,000}{(1+y)^4}$$

?

I am trying to calculate the yield to maturity of a bond, and the answer is 2.66% or 2.67% (depending on your rounding off). I know some other method (some sort of trail and run method), but its rather long in my opinion.

The question was:

A bond has an annual coupon (interest) rate of 8%, with nominal value of 100,000 that has maturity in 4 years time. If the bond sells at 120,000, what is the yield to maturity?

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    Multiply through by $(1+y)^4$. You get a quartic in $1+y$ (even in $y$ if you masochistically expand). There **is** a formula for the roots of a quartic, initially due to Cardano and Ferrari, with variants by a bunch of people. None of these is useful for your purposes. Use a numerical method, like Newton-Raphson. A couple of iterations are enough.2012-09-30

3 Answers 3