Suppose that the following risk-free spot rates prevail in the market: r1=4%, r2=5%, r3=6%, r4=6.5%, where rT denotes the spot rate per annum on an investment with T years to maturity, quoted with annual compounding. You can borrow and lend at these rates. Let f(T1,T2) denote the annual forward rate, quoted with annual compounding, applicable to a forward rate agreement to borrow or lend money in T1 years from today until T2 years from today.

Questions:

1. Compute the forward rate f2,4 that prevails if there are no arbitrage opportunities.
2. You are expecting a USD 1,000 payment in two years from today. You want to invest this money for two years at the appropriate forward rate prevailing today. Unfortunately, you cannot find a market participant willing to enter into a forward loan agreement with you. However, you can borrow and lend at the prevailing spot rates given above. How can you ensure to earn the prevailing forward rate on your future investment?