Investment of the year

At the beginning of the year, my father invested EUR 1,000 in the bank at an annual interest rate of 3%. How many euros will the bank credit him with the deposit after eight months? (compound interest - from financial mathematics)

Correct answer:

x =  19.9013 Eur

Step-by-step explanation:

$$\begin{gathered} a=1000 \\ p=1+3/100=\frac{103}{100}=1.03 \\ a{q}^{12}=p\cdot a \\ q=p^{1/12}=\sqrt[12]{1.03}\doteq 1.0025 \\ x=a\cdot q^8-a=1000\cdot 1.0025^8-1000=19.9013\text{Eur} \end{gathered}$$

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