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 present value of the bond given that the interest rate is presently 10% compounded semi-annually.
There are 6 periods of half a year until maturity.
If the interest rate is the same as the coupon rate.
In other words, the bond is valued at par when the interest rate is equal to the coupon rate.
Now let the interest rate rise to 14%, compounded semi-annually.
This example shows that the value of the bond declines with rising interest rate.