I know that calculations of yield to maturity(YTM) assume that all coupon payments are reinvested at the same rate as the bond's current yield and take into account the bond's current market price, par value, coupon interest rate, and term to maturity.
I was reading a book where the author goes like this - Consider the example of a five-year 10 percent bond paying interest semi-annually which is purchased at par value of 100. If immediately after the bond is purchased, interest rates decline to 5 percent, the bond will initially rise to 121.88 from 100. The bond rises in price to reflect the present value of 10 percent interest coupons discounted at a 5 percent interest rate over five years. The bond could be sold for a profit of nearly 22 percent. However, if the investor decides to hold the bond to maturity, the annualized return will be only 9.10 percent. This is because the interest coupons are reinvested at 5 percent, not 10 percent.
Now, I don't understand this line - "if the investor decides to hold the bond to maturity, the annualized return will be only 9.10 percent". How to calculate and verify this ? Is there any formula/equation for doing that ?