# Yield to Maturity and Yield Curve

![](https://4259454522-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MXMOH6zuTsXTNcMNL-d%2Fuploads%2FrFUkhiss7OxILexH5z5I%2Fimage.png?alt=media\&token=4b008b30-d402-4f8d-ad92-77059420b72f)

After initially providing liquidity to all bond AMM Pools, market forces will determine the bonded Duet discount rates.

Let us assume that bonds with a duration of 12 months with 100 Duet face value are now trading at 49.7 Duets. This implies that the market is pricing a 6% coupon rate per epoch.

Yield to Maturity is the annualized return expected if an investor buys a bond at market price P, reinvests all payments at the current rate, and holds it until maturity.

Given that the current price P is 49.7, payment is 100 and duration is 12, Knowing that **,**$$P=Payment/(1+R)^n$$, Thus

$$
R=\sqrt[n]{Payment/NPV}-1=\sqrt[12]{100/49.7}-1=6\%
$$

Now, to annualize the return, we calculate YTM as

$$
YieldtoMaturity(YTM)=(1+R)^{12}-1=(1+6\%)^{12}-1=101.22\%
$$

Market prices of bonds of all 12 epochs will form an implied yield curve, typically with a higher yield to maturity at longer durations.

**The market mechanisms will balance buying and selling pressures such that when selling pressures of bonds are greater, the market price of bonds will fall, and yield will rise, which will attract more investors to reinvest Duet tokens; when investors reinvest Duet tokens with enthusiasm, bond prices will increase, and yield will fall, which will encourage bondholders to sell their bonds at a profit.**
