it just confused me sunddenly if we are discount the current price of a bond, the maturity is 3 and we know the coupon and we have year 3 YTM why cant we use the YTM but we have to find the spot rate still?

You have to discount back at each spot rate. Not the YTM. In the exam there’s a chance you are not given any spot rates and just the benchmark par rates. If that’s the case you will need to bootstrap each of the par rates to get the correct spot rates and then use the normal formula. C/R1 + C/R2 +(100 +C) /R3

ye i memorized the whole bootstrapping crap, i just wownder why YTM doesnt work, is that because the reinvestment assumption?

You can discount all of the cash flows at the YTM. You don’t need to compute the spot rates.