The annual interest rate of a bond that matures 3 years from now is 4%, while the annual interest rate of a bond that matures 7 years from now is 8%. Some investor wishes to save her/his future income from year 3 to year 7 at a predetermined interest rate. In this situation,

(a) What is the fair interest rate for this forward contract?

(b) Alternatively, we can say that the current price of a bond that matures at year 3 is $0.8890, while the current price of a bond that matures at year 7 is $0.5835. In situation, if an investor wishes to buy the bond that matures at year 7, 3 years later, instead of today, at what price can she/he buy that bond at year 3?

(c) If the investor can buy a bond that matures at year 7 at the price obtained in (b) three year from now, what interest rate she/he would basically earn from that bond? Is that interest the same as the interest rate obtained in (a)?