= Solution
Let $Y_{agpq}$ be the premium at age $a\in\{21,30,40\}$, gender $g\in\{F,M\}$, policy $p\in\{\mathrm{3rd},\mathrm{comp}\}$, and points $q\in\{0,3,6,9\}$, for the combinations actually observed. The additive <normal linear model> is
$$
Y_{agpq}=\mu+\alpha_a+\gamma_g+\delta_p+\eta_q+\varepsilon_{agpq},\qquad \varepsilon_{agpq}\overset{\mathrm{iid}}\sim N(0,\sigma^2).
$$
Its <corner-point constraints> are $\alpha_{21}=\gamma_F=\delta_{\mathrm{3rd}}=\eta_0=0$. Thus $\mu$ is the reference-category mean; the other coefficients are additive contrasts. The model assumes a common variance and excludes all <interactions>. It has $1+2+1+1+3=8$ estimable mean parameters and $32-8=24$ <residual degrees of freedom>. The variance estimate is
$$
\boxed{\hat\sigma^2=19512/24=813.}
$$
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