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.

Hey Mounir, good to see you again. Step 1: Calculate the total rent for the first year. 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 F CFA/month × 12 months/year = 3,000,000 F CFA Step 2: Determine the common ratio for the annual rent increase. 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 Step 3: Identify the parameters for the geometric series. 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 Step 4: Apply the formula for the sum of a geometric series. The sum (S_n) of a geometric series is given by the formula: S_n = a (r^n - 1)/(r - 1) Substitute the values: S_10 = 3,000,000 × (1.05)^10 - 11.05 - 1 S_10 = 3,000,000 × (1.05)^10 - 10.05 Step 5: Calculate the value of (1.05)^10 and the final sum. (1.05)^10 ≈ 1.628894627 Now substitute this value back into the sum formula: S_10 = 3,000,000 × (1.628894627 - 1)/(0.05) S_10 = 3,000,000 × (0.628894627)/(0.05) S_10 = 3,000,000 × 12.57789254 S_10 = 37,733,677.62 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 37,733,677.62 F CFA. Send me the next one 📸