The current term-structure of spot rates is as follows (with con- tinuous compounding):

Maturity (years) Zero-rate(%) 1 3.0 2 4.5 3 5.5

(a) What is the implied forward rate r0(2, 3)?

(b) A bank offers a special bond A through which investors can borrow (lend) $100 in year 2 and repay (receive) $100e

0.07 in year 3. Is there an arbitrage? If so, what is the arbitrages net cash flow in year 0? (Consider an arbitrage strategy where we use one unit of bond A and the net cash flows are zero from years 1 through 3)