Savings

The depositor regularly wants to invest the same amount of money in the financial institution at the beginning of the year and wants to save 10,000 euros at the end of the tenth year. What amount should he deposit if the annual interest rate for the annual interest period is 2% and the interest tax is 19%? Assume that the depositor will not withdraw deposits or interest during the entire savings period and the annual interest rate will always be the same.

Correct answer:

a =  914.43 Eur

Step-by-step explanation:

$$\begin{gathered} r_1=2\mathrm{\%}={\displaystyle \frac{2}{100}}=0.02 \\ {r}_2=19\mathrm{\%}=1-{\displaystyle \frac{19}{100}}=0.81 \\ q=1+r_1\cdot r_2=1+0.02\cdot 0.81=1.0162 \\ 10000=a\cdot q^{10}+a\cdot q^9+a\cdot q^8+a\cdot q^7+a\cdot q^6+a\cdot q^5+a\cdot q^4+a\cdot q^3+a\cdot q^2+a\cdot q \\ a=10000\mathrm{/}(q^{10}+q^9+q^8+q^7+q^6+q^5+q^4+q^3+q^2+q)=10000\mathrm{/}(1.0162^{10}+1.0162^9+1.0162^8+1.0162^7+1.0162^6+1.0162^5+1.0162^4+1.0162^3+1.0162^2+1.0162)=914.43\text{ Eur} \end{gathered}$$

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