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Given that $l_{70}=1000$, $l_{71}=960$, $l_{72}=912$, and the interest rates are at a constant $10%$, calculate $A_{70}(1_2)$.

$$ \begin{array}{c|lcr} \text{Age} & l_x & d_x \\ \hline 70 & 1000 & 0 \\ 71 & 960 & 40 \\ 72 & 912 & 88 \end{array} $$

$A_x(b)=\sum^{w-x-1}_{k=0} b_k. v(k+1). \frac{d_{x+k}}{l_x}$

$=[(1.10)^{-1}. \frac{40}{1000}]+[(1.10)^{-2}. \frac{88}{1000}]=0.109$

But the answer is $0.0760$

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You are double counting $48$ people! Your term $d_2=88$ contains those who died in the first year and those that died in the second year. The correct calculation is \begin{equation*} \frac{1}{1.1}\cdot\frac{40}{1000}+\frac{1}{1.1^2}\cdot\frac{48}{1000}=0.0760 \end{equation*}