The way I understand it buying a simple term annuity from an insurance company is like depositing money in a account that earns fixed interest compounded for the duration of the annuity and taking out the annuity payment every month/year, etc.
Since a bond is an annuity then I would think that the same would apply. That buying a bond is like depositing my principal into an account, and removing the coupon payment every 6 months. Thus the yield to maturity which should be the interest earned on the principal should be fixed for the maturity of the bond. However it is not, and instead requires the investor to reinvest at the ytm.
Why does this explanation seem not to hold for bonds as it does for annuities?