Profitable bank deposit 2012

Calculate the real value lost by depositing €11200 in a bank for 4 years at an interest rate of 2% p.a., with a 19% tax on interest and an annual inflation rate of 3.7%. (Calculate what you lose by leaving money in a bank account at a negative real interest rate. Alternatively, calculate the cost of goods you can buy today and how much the same goods will cost in the future.)

Final Answer:

x =  928.4 €

Step-by-step explanation:

$$\begin{gathered} a=11200\text{eur} \\ u=3.7 \\ {r}_0=100\%-19\%=1-\frac{19}{100}=0.81 \\ {r}_1=2\%=\frac{2}{100}=\frac{1}{50}=0.02 \\ {r}_2=1+r_0\cdot r_1=1+0.81\cdot 0.02=1.0162 \\ {r}_3=100\%-3.7\%=1-\frac{3.7}{100}=0.963 \\ n=4 \\ r=r_2\cdot r_3=1.0162\cdot 0.963\doteq 0.9786 \\ b=a\cdot r^n=11200\cdot 0.9786^4\doteq 10271.6434\text{eur} \\ x=a-b=11200-10271.6434=928.4\text{Eur} \end{gathered}$$

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