B3. The Director promised the new employee Žan that he would receive a salary of 500 euros for the first month, and then each subsequent month his salary would increase by $0.5 \%$. After how many months will his salary exceed 1500 euros? Calculate Žan's average salary over this period (from the first salary to and including the first salary that exceeds 1500 euros).
B3. We consider the compound interest account $G_{t}=G_{1} \cdot r^{t-1}$, where $r=1+\frac{0.5}{100}=1.005$. We write the exponential equation $1500=500 \cdot 1.005^{t-1}$, which we rearrange to $3=1.005^{t-1}$. We logarithmize the equation and get $t=\frac{\log 3}{\log 1.005}+1 \doteq 221.3$. The first payment that will be greater than 1500 euros will be after 222 months. To calculate the average salary, we need to divide the sum of all payments by the number of payments, which is 222. We use the formula for the sum of $n$ terms of a geometric sequence and get $S_{222}=500 \cdot \frac{1.005^{222}-1}{1.005-1} \doteq 202597.76$. We divide the sum by 222. Therefore, the average of Jane's salary is 912.60 euros.

The compound interest account $G_{t}=G_{1} \cdot r^{t-1} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$ point

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Calculation $t=\frac{\log 3}{\log 1.005}+1 \doteq 221.3 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Answer: After 222 months . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 point

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Calculation of the average salary 912.60 euros...................................................... 1 point