# Bond prices tend to 100 at maturity?

Let's assume we have a fixed-income bond, which is paying a yearly coupon. For example a 3 year bond, 1% fixed coupon, issued at par. So we have

at issue -> $Price=\frac{1}{(1+0,01)^1}+\frac{1}{(1+0,01)^2}+\frac{101}{(1+0,01)^3}=100$

Now, when I am near maturity I think this should be something like

$Price=\frac{101}{(1+0,01)^{0.0001}} \simeq 101$

But it seems market prices tend to be 100 near maturity. You can see for example

Which one is correct?

• Are you mixing up clean and dirty prices? The clean price tends to 100 as maturity approaches but the dirty price converges to 101. – LocalVolatility Dec 5 '17 at 21:37
• ok so that formula is dirty price, clean price is $CleanPrice=DirtyPrice-AccruedInterest$ where Accrued Interest is $Notional*Coupon_y*\frac{D}{D_y}$ $D$: days from last coupon, $D_y$: days in a year so AI tend to 1 (in my example) while $D\rightarrow D_y$ – Castore Dec 5 '17 at 22:00