Question

The cost of erecting the ground floor of a building is $35000. The cost of adding an extra floor increases by 5% for each extra floor. Find the total cost of erecting 5 floors (including the ground floor )

Answer 1

To find the total cost of 5 floors with a 5% cost increase per floor, you calculate the cost for each floor and sum them up, resulting in a total cost of $193,397.09.

Step-by-step explanation:

To calculate the total cost of erecting 5 floors including the ground floor, we start with the cost of the ground floor and then calculate the increased cost for each additional floor. The cost increase is given as a 5% increase per additional floor.

The cost of the ground floor is $35,000. For each subsequent floor, the cost is multiplied by a factor of 1.05 (to account for the 5% increase). This can be represented by a geometric series.

The total cost T for 5 floors can be calculated as:

• T = $35,000 + $35,000 × 1.05 + $35,000 × 1.05² + $35,000 × 1.05³+ $35,000 × 1.05⁴

We can calculate the exact cost for each floor and add them up to find the total cost:

• 1st Floor (Ground Floor): $35,000
• 2nd Floor: $35,000 × 1.05 = $36,750
• 3rd Floor: $35,000 × 1.05² = $38,587.50
• 4th Floor: $35,000 × 1.05³ = $40,516.88
• 5th Floor: $35,000 × 1.05⁴ = $42,542.71

Adding these amounts we get the total cost T:

• T = $35,000 + $36,750 + $38,587.50 + $40,516.88 + $42,542.71
• T = $193,397.09

Answer 2

The total cost of erecting 5 floors, including the ground floor, is $44,843.75.

Step-by-step explanation:

To calculate the total cost of erecting 5 floors, including the ground floor, we need to consider the initial cost of the ground floor and the incremental cost for each additional floor. The cost increases by 5% for each extra floor. We can use the formula for compound interest to find the total cost.

Let P be the principal amount (initial cost of the ground floor), r be the rate of increase (5% or 0.05), and n be the number of extra floors.

The formula for compound interest is given by:

`\[ A = P * (1 + r)^n \]`

In this case, the total cost (A) is the amount we're trying to find. Substituting the given values:

`\[ A = $35,000 * (1 + 0.05)^4 \]`

Calculating this expression gives us the total cost of erecting 5 floors, including the ground floor. Therefore, the total cost is $44,843.75.

In conclusion, starting with the initial cost of $35,000 for the ground floor, the incremental cost for each additional floor, compounded at a rate of 5%, results in a total cost of $44,843.75 for erecting 5 floors, including the ground floor. This calculation accounts for the compounding effect of the 5% increase for each additional floor, providing a comprehensive understanding of the total expenditure.