The expectation of the rate in the Vasicek model after T years is given by:

$$r_0 e^{-kT} + \theta(1 - e^{-kT})$$

Where:

• $r_0 =$ current interest rate
• $k =$ mean reversion parameter
• $\theta =$ long-run value of the short-term rate assuming risk neutrality
• $T =$ time in years

First, we must work out the value of $\theta$

$$\theta \approx r_1 + \frac{\lambda}{k} \approx 6\% + \frac{0.35\%}{0.03} = 17.67\%$$

$r_1$ is true long-term interest rate, and $\lambda$ is the annual drift

Thus,

the expected rate after 10 years
$= 5\% e^{-0.03 \times 10} + 17.67\%(1 - e^{-0.03 \times 10})$
$= 3.7041\% + 4.5797\%$
$= 8.2838\%$