theoretical spot rate???

Hi folk, Please help me figure out where I am going wrong with this question. An investor has a 1-year, semiannual, 10% coupon bond which is priced at $1,025. If the 6-month spot rate on a bond-equivalent basis is 8%, the 1-year theoretical spot rate as a BEY is: 7.3% is the answer. I keep coming up with 8.99%. Here’s how: (1.04)(1.05)^0.5= 1.044988-1= .04498 x 2= .089976 Where am I going wrong here?

PMT 50, FV 1000, PV -1025 N2, solve for I= 3.6 times 2 = 7.6 I think.

1025 = 50/1.04 + 1050/X^2 3.67% multiply by 2–> 7.34 CP

are we supposed to use: 1.025=10/(1+4%)+1010/(1+x)^2 solve for x and then *2?

When they say spot rate, you know you need to use different spot rate for each cash flow. So 1025 = 50/1.04 + 1050/ ((1+ x/2) ^ 2). X = 7.34;

On the exam, would you usually use the bootstrapping method (please see cpk123’s post above) whenever the bond price is involved? And then use the method I used whenever the question simply asks for a forward rate? Thanks.