# Time to maturity of a bond not divisible by payment period

I am relatively new to the topic of quantitative finance - at the classes I got an exercise about "2.5 year bond payed annually". Therefore I have a question about the time of payment of interest. The first payment will be payed after half a year or after a year? In other words, does the scedule of payment looks like 1/2, 1.5, 2.5 or rather like 1, 2, 2.5?

## 2 Answers

As a general rule, unless told otherwise, start at the maturity date of the bond and work backwards: the last coupon payment will be at maturity, the one before will be 1 year earlier, then 1 year before that, and so on.

There are exceptions and special cases, but they would probably not occur in a simple example from a book. Most likely this is an ordinary yearly bond which has been purchased halfway between coupon payments, so the next coupon is 0.5 years away.

In general when payment frequency and tenor don't align, you can introduce a shorter period (called a stub) for one period. This can be at the beginning of the schedule or the end of the schedule. As far as I know, at the beginning is far more customary (because then you can 'forget' about weird periods earlier), but both do occur. Another alternative is to have a longer than normal period, but this happens less afaik.

So my best guess would be 0.5, 1.5 and 2.5, but there are a lot of variations possible.