can you explain how to arrive at answer as well i found a si

can you explain how to arrive at answer as well. i found a similar question on here but can not figure out how answer was derived

QUESTION 19 Unbiased Expectations Theory Suppose that the current one-year rate (one -year spot rate) and expected one-year T-ill rates over the following three years e, years 2, 3, and 4 respectively) are as follows IR,-5%, Een)-5.5%, EGri)-6.5% E(4r)-700% jsing the unbiased expeciations theory, what is the current (long term) rate for tour year-maturity Treasury securities? 6 33 percent 6.75 percent 7 00 percent 6 00 percent

Solution

Unbiased Expectations Theory states that current long-term interest rates contain an implicit prediction of future short-term interest rates.

Current rate for four year maturity treasury securities = [( 1 + 0.05)( 1 + 0.055)(1 + 0.065)(1 + 0.07)]^1/4 - 1

Current rate for four year maturity treasury securities = [ 1.262337 ]^1/4 - 1

Current rate for four year maturity treasury securities = 1.05997 - 1

Current rate for four year maturity treasury securities = 0.05997 or 6.00 percent

When you get 1.262337 on screen, use the following keys to get 1.05997 :

y^x

4

1/x

=