Spot rate calculation question

I am felling a little ignorant right now & need some help understanding spot rate calculations. Here is the question: An investor gathers the following information about a 3-year, annual-pay bond: * Par value of $1,000 * Coupon of 8% * Current price of $1,100 * 1-year spot interest rate is 5% * 2-year spot interest rate is 6% Using the above information, the 3-year spot rate is closest to: A) 4.37% B) 4.27% C) 8.20% The correct answer is B) 4.27%. The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $80 (0.08 × 1,000) and the face value is $1,000. Hence, bond price of 1,100= 80/(1.05)+ 80/(1.06)2 + 1,080/(1 + 3-year spot rate)3. Using the y^x key on our calculator, we can solve for the 3-year spot rate of 4.27%. I understand how to find the PV of the CF’s using the spot rates for year 1 & 2, but I just can’t figure how using the y^x key will let me solve for 4.27%. Any help would be greatly appreciated.

Hi SharpeCFA, I assume you are using TI BA II plus,here is the calculation: you already have the equation for PV of the Bond : 1,100= 80/(1.05)+ 80/(1.06)^2 + 1,080/(1 + 3-year spot rate)^3 =>952.63=1080/ (1 + 3-year spot rate)^3 let 3-year spot rate=X =>(1+X)^3=1080/952.63 =>(1+X)=(1.1337)^1/3 (cube root of 1.1337) =>1.1337 press [Y^X] press [(] enter [1/3] press [)]press [=] =>1.0427 here’s the answer Hope I made it clear. Cheers Dhruv

Thank you very much Dhruv! This makes complete sense now.