Compare these examples with those in Finance[levelcoupon] I hold a bond with face value of 1000 units with an annual coupon rate of 12%. The coupon is paid twice yearly. The maturity is in 3 years. What is the yield to maturity of the bond, compounded semiannually given that its present value is 1050.75 units?
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$\mathrm{with}\left(\mathrm{Finance}\right)\:$

There are 6 periods of half a year until maturity.
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$\mathrm{yieldtomaturity}\left(1050.75\,1000\,\frac{0.12}{2}\,6\right)$

Yield is 5% per half year, therefore it is
10% per year. If the present value is the same as the face value
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$\mathrm{yieldtomaturity}\left(1000\,1000\,\frac{0.12}{2}\,6\right)\cdot 2$

In other words, the yield is identical to the coupon rate when the bond is valued at par. (Remember that the extra factor of 2 is to convert the semiannual yield to annual yield).
Now let the present value decline to less than face.
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$\mathrm{yieldtomaturity}\left(952.33\,1000\,\frac{0.12}{2}\,6\right)\cdot 2$

This example shows that the yield must increase when the value of the bond declines.