The machine

The annual depreciation of the machine is 10%. After eight years, the machine is worth 697 euros. What was the price of this machine at the time of purchase?

Correct answer:

a₁ =  1619.17 Eur

Step-by-step explanation:

$$\begin{gathered} q=100\%-10\%=1-\frac{10}{100}=0.9 \\ {a}_9=697\text{Eur} \\ n=8 \\ a(n)=a_1\cdot q^n \\ {a}_1=a_9/q^n=697/0.9^8\doteq 1619.1709\text{Eur} \\ \text{ Verifying Solution: } \\ {a}_2=q\cdot a_1=0.9\cdot 1619.1709\doteq 1457.2539 \\ {a}_3=q\cdot a_2=0.9\cdot 1457.2539\doteq 1311.5285 \\ {a}_4=q\cdot a_3=0.9\cdot 1311.5285\doteq 1180.3756 \\ {a}_5=q\cdot a_4=0.9\cdot 1180.3756\doteq 1062.3381 \\ {a}_6=q\cdot a_5=0.9\cdot 1062.3381\doteq 956.1043 \\ {a}_7=q\cdot a_6=0.9\cdot 956.1043=\frac{69700}{81}\doteq 860.4938 \\ {a}_8=q\cdot a_7=0.9\cdot 860.4938=\frac{6970}{9}\doteq 774.4444 \\ {a}_9=q\cdot a_8=0.9\cdot 774.4444=697 \end{gathered}$$

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