$$ Suppose you buy a $50-$year, $5\mathrm{.}5\%$ coupon bond when its YTM is $6\mathrm{.}67\%$ and you plan to hold it for $15$ years. You forecast that the YTM will be $7\mathrm{.}5\%$ when it is sold and the reinvestment rate on coupon payment will be $3\mathrm{.}2\%.$ What is your realized return over $10$ years of investment? Assume that bond pays semi$-$annual coupon payment

How much do you pay for the bond?

How much can you sell you bond after $15$ years at the YTM of $7\mathrm{.}5\%?$

What is the total value of your coupon payments at the end of $15$ years with reinvestment rate of $3\mathrm{.}2\%?$

What is your realized return over $15-$year period?