Bond is maturing in 10.25 years, YTM calculation
Bond is maturing in 10.25 years and has an annual coupon rate 4.15% paid semiannually and price 92-12+
I need to calculate yield to maturity
Ok so I know that 92-12+ is basically 92 + 12/32 + 1/64 = 92.390625.
Now here comes the yield to maturity confusion. Normally I’d expect to have the maturity time to be divisible by the compounding rate, but 10.25 is not divisible by 0.5 which confuses me.
The formula for YTM (let $ y $ be the YTM) if my memory serves me well is this:
$ \sum_{n=1}^{20} \frac{2.075}{(1+0.5y)^n} + \frac{100}{(1+0.5y)^{20.5}} = 92.390625 $
But the last summand confuses me abit. Is this actually correct?
The first coupon occurs 0.25 years from now, the next 0.75 years from now, the twentieth and last 10.25 years from now. So no, the equation is not correct. You can only use your formula on a coupon date and today is not a coupon date. You could calculate PV at time 0.25 and then discount to the present (i.e. half a period):
$$ \frac{1}{1+0.25y}\left(\sum_{n=1}^{20} \frac{2.075}{(1+0.5y)^{n-1}} + \frac{100}{(1+0.5y)^{19}}\right) = 92.390625. $$