a
There are two ways that you can get from today to five years from today:
- 5-year spot rate
- 2-year spot rate, 1-year forward rate starting in 2 years, 2-year forward rate starting in 3 years
If you invest USD1,000 at the 5-year spot rate, at the end of 5 years you’ll have:
USD1,000(1.059)^5 = USD1,331.91
If you invest USD1,000 at the 2-year spot rate, then the 1-year forward rate, then the 2-year forward rate, you’ll have:
USD1,000(1.053)²(1.057)(1.052)² = USD1,297.07
Thus, the way to make money is to borrow at the 2-year spot/1-year forward/2-year forward rates and lend at the 5-year spot rate; you’ll make:
USD1,331.91 – USD1,297.07 = USD34.86 (in 5 years).
(Note that the USD1,000 is a red herring: for arbitrage you don’t need any money because you’re borrowing and lending the same amounts; that’s why it’s risk-free.)
You have to solve:
(1.053)²(1 + 1f2)(1.052)² = (1.059)^5
1 + 1f2 = (1.059)^5/((1.053)²(1.052)² = 1.085404
1f2 = 8.5404%
Now that I can understand the exercise. Your instruction was very clear and helpful
Thank you so much for your help 
I’m glad that it was.
My pleasure.