Financial economics: Bond Price I know that if the coupon rate on a bond is larger than the yield-to-maturity, then the price must be higher than the par value. Yet I have the bond price equation $P=\frac{c}{y}\left(1-\frac{1}{(1+y)^T}\right)+\frac{Par}{(1+y)^T}$, and I wonder how I manipulate this equation to show that what I mentioned above is correct. Grateful for any tips to solve this.
Set the inequality $P&gt;Par$, substitute the bond price equation, and then manipulate the inequality to find your result:

$$P&gt;Par$$
$$\frac{c}{y}\left(1-\frac{1}{(1+y)^T}\right)+\left(\frac{Par}{(1+y)^T}\right)&gt;Par$$
$$\frac{c}{y}\left(1-\frac{1}{(1+y)^T}\right)&gt;Par\left(1-\frac{1}{(1+y)^T}\right)$$
$$\frac{c}{y}&gt;Par$$

Let $c=r_cPar$ so that $r_c$ is the coupon rate (this is the fraction of the Par value that the coupon represents. Then the last equality is equivalent to

$$r_c&gt;y$$

Therefore, the first inequality is true if and only if all of the following inequalities are. In particular, the last inequality gives the result you are looking for.