First compute the present value factor sum for the bond cash flows using the spot rates:

$$A = e^{-0.02\cdot 0.5} + e^{-0.03\cdot 1.0} + e^{-0.04\cdot 1.5} + e^{-0.05\cdot 2.0} = 3.80710$$

For a par bond, the coupon rate under semiannual coupons is:

$$\text{Par yield (semiannual)} = \frac{1 - e^{-0.05\cdot 2.0}}{A} \times 2 = 4.99922\%$$

Convert that semiannual yield to a continuously compounded yield:

$$2\ln\left(1 + \frac{4.99922\%}{2}\right) = 4.94\%$$

Therefore, the two-year par yield with continuous compounding is 4.94%.