I am unable to understand the steps. Hence, can you provide with a explanation and step by step guide to this question

7) At your favorite bond store, Bonds-R-Us, you see the following prices: a. 1-year $100 zero selling for $90.19 b. 3-year 10% coupon $1000 par bond selling for $1000 c. 2-year 10% coupon $1000 par bond selling for $1000 Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity or maturity premium exists, and the bonds are equally risky. What is the implied l-year rate two years from now? Solution: From (a), you know that the 1-year rate today is 10.877%. Using this information, (c) tells you that: 1000 = 100/1.10877 + 1100/(1 + 2-year rate)2 So, the 2-year rate today is 9.95%. Using these two rates, (b) tells you that: 1000 = 100/ 1.10877 + 100/1.O9952 + 1100/(1 + 3-year rate)3 So, the 3-year rate today is 9.97% l-year rate 2 years from now = (3 x 9.97% 2 x 9.95%) = 10.01%