I need to calculate the yield of a 2 year Coupon Bond. Price = 98, Coupon = 3.5, N = 100.

Now when I try to solve this, I arrive at the equation: $$ 98 = 3,5*e^{-y}+103,5*e^{-2*y} $$ But I can't figure out how to solve this equation for the yield y. I tried with Wolfram Alpha but don't know how to interpret the result. Is my math just too rusty or is my approach wrong?

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    $\begingroup$ You indeed need to solve that equation numerically (say Newton Raphson). WolframAlpha gives you the right solution: $y\approx 0.0446774 \approx 4.5\%$ wolframalpha.com/input/… $\endgroup$ – Kevin Jul 6 '20 at 15:31
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    $\begingroup$ @KeSchn No. It is just a quadratic equation in disguise! $\endgroup$ – stackoverblown Jul 6 '20 at 19:50
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    $\begingroup$ @stackoverblown you and ir7 are, of course, absolutely right :) $\endgroup$ – Kevin Jul 6 '20 at 19:53

Hint: Let $$z = \mathrm{e}^{-y} $$

That way you get a quadratic equation in $z$ (note that $z$ is positive) and then you can get back to $y$ using:

$$ y = -\ln (z) $$


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