Why would the principal be calculated as a semi-annual return when its just the coupon payments that are being paid semi-annually?

Assume you took your principal and bought a semi annual interest bearing security. since you could invest that money elsewhere and earn semi-annual compounding interest, it would be nice to know what the fair price for the principal is in terms of present value.for example, if the bond has a coupon rate of 10% and matures in 5 years and pays interest semi-annually, a fair price for the $100 principal would be $61.39. why doesthis make sense? because you could turn away from the issuer and turn toward a competitor that offers semi-annual compounding interest based on the same terms mentioned above:$61.39 + 5% + 5% + 5% + 5% + 5% + 5% + 5% + 5% + 5% + 5% = $100but what if you invested your principal in a bond that paid interest annually, had a coupon rate of 10% and matured in 5 years? a fair price would be $62.09. why does thismake sense? because you could turn away from the issuer and turn toward a competitor that offers annual compounding interest based on the same terms:$62.09 + 10% + 10% + 10% + 10% + 10% = $100so if you turn back to the first scenario where $61.39 is a fair price based on the terms of the investment, but you decide to offer $62.09, the seller will gladly accept the extra money, knowing that you are paying more than you should for what the issuer is offering you.