Question

1) Nagy bought a bond that has a face value 150,000 EGP that gives 7 % of its face value each 6 months. The bond duration is 10 years. Its redemption value is 150,000 EGP. Nagy sold the bond to Sameh after 6 years at 160,000 EGP. Determine the annual interest rate for both Nagy and Sameh.

Answer 1

Nagy bought the bond at face value i.e. 150,000 EGP which gave him 7% return of face value as coupon payments every 6 months. Or in annual terms we can say that Nagy got 14% of the face value in coupon payments. This amounts to:

Thus, the annual coupon payment to Nagy is 21,000 EGP and annual interest rate is 14%.

Now, Nagy sells the bond to Sameh after 6 years at 160,000 EGP. It is to be noted that the coupon payments will remain the same, regardless of the new price of the bond. And it will remain equal to 21,000 EGP annually. The annual interest rate that Sameh will get is whatever percentage 21,000 is of the bond price i.e. 160,000 EGP.

Thus, annual interest rate for Sameh is:

Thus, Sameh's annual interest rate is 13.125 %. We can also see that bond prices and interest rate is inversely related with this example.

Thanks!