Problem:

The effective annual yield on a one-year zero coupon bonds is 7% and the effective annual interest rate on a two-year zero coupon bond is 8%. You are able to arrange a one-year forward investment at rate i for a one-year period. Suppose that under these conditions it is possible to make a riskless profit with the following strategy:

(i) Invest amount 1 for one year at 7% effective annual

(ii) Borrow amount 1 for 2 years at 8% per year effective annual

(iii) Using the proceeds from (i), arrange a one-year forward one-year length investment of amount 1.07 at rate i (starting one year from now)

(iv) Use the proceeds from (iii) to repay loan (ii) at the end of the second year. For what full range of i will this strategy result in a positive amount left over after all 3 transactions are settled at the end of the second year?

Please explain in detail and show all work.