Deposit in the bank

After the summer job, you saved € 800 in the bank. The interest rate is 4% p. a. Interest on the deposit is taxed at 15% withholding tax. How much can you withdraw after three months?

Correct answer:

x₃ =  806.8193 Eur

Step-by-step explanation:

$$\begin{gathered} a=800\text{eur} \\ {q}_1=4\%=\frac{4}{100}=\frac{1}{25}=0.04 \\ {q}_2=100\%-15\%=1-\frac{15}{100}=0.85 \\ q=1+\frac{q_1}{12}\cdot q_2=1+\frac{\frac{1}{25}}{12}\cdot \frac{17}{20}\doteq 1.0028 \\ {x}_1=a\cdot q=800\cdot 1.0028=\frac{12034}{15}\doteq 802.2667 \\ {x}_2=x_1\cdot q=802.2667\cdot 1.0028\doteq 804.5398 \\ {x}_3=x_2\cdot q=804.5398\cdot 1.0028=806.8193\text{Eur} \end{gathered}$$

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