Modified duration = $\frac{\text{Macaulay duration}}{1 + \frac{y}{m}}$

Where $y$ is the yield and $m$ is the compounding frequency per annum. We first calculate the Macaulay duration:

Macaulay duration = $\frac{\sum_{t=1}^{n} \text{PV}(C_t) T}{\text{Market Price of Bond}}$

Where $\text{PV}(C_t)$ is the present value of coupon payments at time $t$, and $T$ is the time to maturity.

Price of the bond = $\frac{50}{1.03^1} + \frac{50}{1.03^2} + \frac{50}{1.03^3} + \frac{1050}{1.03^4} = 1074.34$

Thus,

Macaulay duration = $\frac{1}{1074.34} \times \frac{50}{1.03^1} + \frac{2}{1074.34} \times \frac{50}{1.03^2} + \frac{3}{1074.34} \times \frac{50}{1.03^3} + \frac{4}{1074.34} \times \frac{1050}{1.03^4} = 3.73412$

And so the modified duration is given by:

Modified duration = $\frac{\text{Macaulay duration}}{1 + \frac{y}{m}}$
= $\frac{3.73412}{1 + \frac{0.03}{1}}$
= $3.62535 \approx 3.62$