R can be solved using the following equation:

$\frac{30}{1 + \frac{0.025}{2}} + \frac{30}{\left(1 + \frac{0.030}{2}\right)^2} + \frac{30}{\left(1 + \frac{0.035}{2}\right)^3} + \frac{1030}{\left(1 + \frac{R}{2}\right)^4} = 1,060$

$\Rightarrow \frac{1030}{\left(1 + \frac{R}{2}\right)^4} = 1,060 - 87.22 = 972.78$

$\Rightarrow \left(1 + \frac{R}{2}\right) = \left(\frac{1,030}{972.78}\right)^{\frac{1}{4}} = 1.0144$

Thus,

$R = 0.0144 \times 2 = 0.0288 = 2.88\%$

The bond pays semi-annual coupons of 6%/2 × 1,000 = USD 30, plus the face value of USD 1,000 at maturity (total of USD 1,030 in period 4). Each known cash flow is discounted using the corresponding zero-coupon rate, and the resulting present values (87.22) are subtracted from the bond price (1,060) to solve for the unknown two-year zero-coupon rate R.