Assume the pure expectation hypothesis holds and the market

Question

Looking in today’s newspaper, you observe the following yield curve information:

Maturity.........Yield

1-Year.......... 4.00%

2-Year.......... 4.50%

3-Year.......... 5.10%                   

4-Year.......... ????%

5-Year.......... 5.50%

Assume the pure expectation hypothesis holds and the market expects that 1-year rate will be 6.1% 4 years from today (4r_t1=6.1%). What is the 4-year rate today (r_t4)? Show every step of your calculations.