Bank Interest Over Months

On January 2nd, 2009, Johnny's father deposited €3,000 in the bank's passbook. The bank provides an annual interest of 0.30% for deposits up to €5,000. However, Johnny's father collected the money after eight months. What is interest in euros added to it?

Final Answer:

x₁ =  5.997 Eur
x₂ =  6 Eur

Step-by-step explanation:

$$\begin{gathered} p=0.30/100=\frac{3}{1000}=0.003 \\ q=\sqrt[12]{1+p}=\sqrt[12]{1+0.003}\doteq 1.0002 \\ {x}_1=3000\cdot q^8-3000=3000\cdot 1.0002^8-3000=5.997\text{Eur} \end{gathered}$$

$x_2=3000\cdot p\cdot \frac{8}{12}=3000\cdot 0.003\cdot \frac{8}{12}=6\text{Eur}$

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