# 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?

$$\frac{1}{1+0.25y}\left(\sum_{n=1}^{20} \frac{2.075}{(1+0.5y)^{n-1}} + \frac{100}{(1+0.5y)^{19}}\right) = 92.390625.$$
• Thank you very much for your reply. Let me just make sure of something: is it correct to discount like that provided that our rate isn't continuous? As in, I was sure that it only worked for continuous compounding, I guess I should go back to the textbooks ... I mean, I remember that there is a relation for rates, like $1 + x = (1 + 0.5x)^2$ if we want to find the semi-annual rate from the annual rate. Shouldn't we apply the same here if we want to discount by a quarter using the semiannual rate $y$? – Makina Dec 16 '18 at 18:17