The amortization amount in the first term is #\euro# #85000#

We have to write off #\euro \, 440000-20000=420000#. This is written off over #5# years. We will name the installment #a#. Since the installment decreases by #\euro \, 500# each time, we must have:
\[a+(a-500)+(a-1000)+\cdots+(a-2000)=420000\]
On the left hand side of the equation we have the sum of #n=5# terms of an arithmetic sequence with #v=-500#. Moreover we have #t_1=a# and #t_{5}=a-2000#. According to the sum formula for an arithmetic sequence the left hand side is equal to \[\frac{1}{2} \cdot n \cdot (t_1+t_n)=\frac{1}{2} \cdot 5 \cdot(a+a-2000)=5\cdot a-5000\]
Hence, we have:
\[5\cdot a-5000=420000\]
This is a linear equation with unknown #a#. It can be solved as follows:
\[\begin{array}{rcl}
5\cdot a-5000&=&420000\\
&& \phantom{xxxxx}\color{blue}{\text{the original equation}}\\
5 \cdot a&=&425000\\
&& \phantom{xxxxx}\color{blue}{\text{added } 5000 \text{ to both sides}}\\
a &=& 85000\\
&& \phantom{xxxxx}\color{blue}{\text{both sides divided by }5}\\
\end{array}\]

We conclude that the amortization amount in the first term is #\euro \, 85000#.