A property is rented for 10 years. The first year's rent is 250,000 F CFA per month. The rent increases by 5% each year. Calculate the total rent paid over 10 years.

The monthly rent for the first year is 250,000 F CFA. Since there are 12 months in a year, the total rent for the first year ($C_1$) is:

$$C_1 = 250,000 \text{ F CFA/month} \times 12 \text{ months/year} = 3,000,000 \text{ F CFA}$$

The rent increases by $5\%$ each year. This means the rent for a given year is $105\%$ of the previous year's rent. The common ratio ($r$) is:

$$r = 1 + 0.05 = 1.05$$

The total duration of the location-vente is 10 years. This means we need to sum 10 terms of a geometric series.

• First term ($a$) = $C_1 = 3,000,000$ F CFA
• Common ratio ($r$) = 1.05
• Number of terms ($n$) = 10 years

The sum ($S_n$) of a geometric series is given by the formula:

$$S_n = a \frac{r^n - 1}{r - 1}$$

Substitute the values:

$$S_{10} = 3,000,000 \times \frac{(1.05)^{10} - 1}{1.05 - 1}$$ $$S_{10} = 3,000,000 \times \frac{(1.05)^{10} - 1}{0.05}$$

$$(1.05)^{10} \approx 1.628894627$$

Now substitute this value back into the sum formula:

$$S_{10} = 3,000,000 \times \frac{1.628894627 - 1}{0.05}$$ $$S_{10} = 3,000,000 \times \frac{0.628894627}{0.05}$$ $$S_{10} = 3,000,000 \times 12.57789254$$ $$S_{10} = 37,733,677.62 \text{ F CFA}$$

The total amount to pay for acquiring the apartment over 10 years is approximately 37,733,677.62 F CFA.

The total cost is $\text{37,733,677.62 F CFA}$.