William has been contracted to paint a school classroom. The classroom is 20m long, l5m
wide and 5m high. There are four windows (2m by 3m) and a door (2m by lm).
1.What is the cost of painting the ceiling at N$6.50 /m'z?
2.What is the cost of painting the walls (excluding the windows and door) at N$8.50
lm2?
3.What is the cost of tiling the floor using tiles (20cm by 20cm) that are sold in boxes
of 50 tiles each at N$50 per box?
4What is the cost of providing air conditioning for this classroom at N$60/m3?
(a)(i) Using the formula for calculating monthly payments on a loan, we have:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
where:
P = monthly payment
L = loan amount
c = monthly interest rate = annual interest rate/12
n = total number of monthly payments
For George's loan, L = N$850,000 and n = 25 years x 12 months/year = 300 months. The monthly interest rate, c, can be calculated as follows:
c = 12%o p.a. / 12 months = 1%o per month
Substituting these values into the formula, we get:
P = 850000[0.01(1 + 0.01)^300]/[(1 + 0.01)^300 - 1] ≈ N$8,919.31
Therefore, George's monthly instalment is approximately N$8,919.31 per month.
(a)(ii) Increasing the payback period to 30 years would result in a total of 30 years x 12 months/year = 360 monthly payments. Using the same formula as above, but with n = 360, we get:
P = 850000[0.01(1 + 0.01)^360]/[(1 + 0.01)^360 - 1] ≈ N$7,517.36 per month
Reducing the interest rate by 15% p.a. would result in a new monthly interest rate of:
c = (12%o p.a. - 15%o p.a.)/12 months = -0.25%o per month
Using the original loan amount and payback period, but with this new monthly interest rate, we get:
P = 850000[(-0.0025)(1 - 0.0025)^300]/[(1 - 0.0025)^300 - 1] ≈ N$6,638.77 per month
Therefore, George's monthly instalments for the increased payback period and reduced interest rate options are N$7,517.36 per month and N$6,638.77 per month, respectively.
(a)(iii) To calculate how much George saves per month using the cheapest option, we need to compare the monthly instalment for each option to the original monthly instalment of N$8,919.31.
The increased payback period option results in a monthly saving of:
N$8,919.31 - N$7,517.36 = N$1,401.95 per month
The reduced interest rate option results in a monthly saving of:
N$8,919.31 - N$6,638.77 = N$2,280.54 per month
Therefore, George would save more money per month by choosing the reduced interest rate option.
1. The surface area of the ceiling can be calculated as follows:
SA = length x width = 20m x 15m = 300m2
Therefore, the cost of painting the ceiling would be:
300m2 x N$6.50/m2 = N$1,950
2. The surface area of the walls (excluding the windows and door) can be calculated as follows:
SA = (height x length) x 2 + (height x width) x 2
SA = (5m x 20m) x 2 + (5m x 15m) x 2
SA = 200m2 + 150m2
SA = 350m2
Therefore, the cost of painting the walls would be:
350m2 x N$8.50/m2 = N$2,975
3. The area of the floor can be calculated as follows:
Area = length x width = 20m x 15m = 300m2
The number of tiles required can be calculated by dividing the area by the area of each tile:
Number of tiles = Area of floor / Area of each tile
Number of tiles = 300m2 / (0.2m x 0.2m) = 7,500 tiles
Since each box contains 50 tiles, the number of boxes required would be:
Number of boxes = Number of tiles / Tiles per box
Number of boxes = 7,500 tiles / 50 tiles per box = 150 boxes
Therefore, the cost of tiling the floor would be:
150 boxes x N$50/box = N$7,500
4. The volume of the classroom can be calculated as follows:
Volume = length x width x height = 20m x 15m x 5m = 1,500m3
Therefore, the cost of providing air conditioning would be:
1,500m3 x N$60/m3 = N$90,000
(a) George is buying a house for N$850,000. He has to pay a
from his bank repayable over 25 years at l2%o p.a. interest.
(i) What is his monthly instalment?
(l) 30 year payback period
(2) Reduced interest rate
l0% deposit and can secure a bond
(ii) Another bank is now giving him two other options i.e. to increase the payback period to 30
years or to reduce the rate by 15% p.a. Find the monthly instalment for each option.
(iii) How much money will he save per month using the cheapest option? (4 marks)
To calculate the cost of painting the ceiling, we need to calculate the area of the ceiling first.
1. Area of the ceiling = length x width
Area of the ceiling = 20m x 15m = 300m²
Cost of painting the ceiling = Area of the ceiling x cost per square meter
Cost of painting the ceiling = 300m² x N$6.50/m²
To calculate the cost of painting the walls (excluding the windows and door), we need to calculate the area of the walls.
2. Area of the walls = 2 x (length x height) + 2 x (width x height) - area of windows - area of door
Area of the windows = 4 windows x (2m x 3m)
Area of the windows = 4 x 6m²
Area of the door = 1 door x (2m x 1m)
Area of the door = 2m²
Area of the walls = 2 x (20m x 5m) + 2 x (15m x 5m) - 4 x 6m² - 2m²
Cost of painting the walls = Area of the walls x cost per square meter
Cost of painting the walls = (area of walls excluding windows and door) x N$8.50/m²
To calculate the cost of tiling the floor, we need to calculate the area of the floor in square meters.
3. Area of the floor = length x width
Area of the floor = 20m x 15m
Now we can find the number of tiles needed. Each tile is 20cm x 20cm, which is 0.2m x 0.2m.
Area of one tile = 0.2m x 0.2m = 0.04m²
Number of tiles needed = Area of the floor / Area of one tile
Number of tiles needed = (20m x 15m) / (0.2m x 0.2m)
Since tiles are sold in boxes of 50, we need to calculate the number of boxes needed.
Number of boxes needed = Number of tiles needed / 50
Number of boxes needed = (Area of the floor / Area of one tile) / 50
Cost of tiling the floor = Number of boxes needed x cost per box
Cost of tiling the floor = (Number of tiles needed / 50) x N$50
To calculate the cost of providing air conditioning, we need to calculate the volume of the classroom.
4. Volume of the classroom = length x width x height
Volume of the classroom = 20m x 15m x 5m
Cost of providing air conditioning = Volume of the classroom x cost per cubic meter
Cost of providing air conditioning = (20m x 15m x 5m) x N$60/m³
Please note that the above calculations are based on the given dimensions and prices.
To find the answers to these questions, we will need to calculate the areas that need to be painted and tiled. Let's break it down step by step:
1. Cost of painting the ceiling:
The area of the ceiling is the same as the floor, as it is rectangular. To find the area of the ceiling, we multiply the length and width: 20m x 15m = 300m².
To calculate the cost of painting the ceiling, we multiply the area (300m²) by the cost per square meter (N$6.50): 300m² x N$6.50 = N$1,950.
2. Cost of painting the walls (excluding windows and doors):
To find the area of the walls, we need to calculate each wall separately. The classroom has 4 walls, with dimensions of 20m (length) x 5m (height) and 15m (width) x 5m (height). So we have:
- Wall 1: 20m x 5m = 100m²
- Wall 2: 20m x 5m = 100m²
- Wall 3: 15m x 5m = 75m²
- Wall 4: 15m x 5m = 75m²
The total area of the walls is 100m² + 100m² + 75m² + 75m² = 350m².
To calculate the cost of painting the walls, we multiply the total area (350m²) by the cost per square meter (N$8.50): 350m² x N$8.50 = N$2,975.
3. Cost of tiling the floor:
The area of the floor can be calculated by multiplying the length and width: 20m x 15m = 300m².
To calculate the number of tiles needed, we need to convert the size of the tiles to square meters. Each tile is 20cm x 20cm, which is equal to 0.2m x 0.2m = 0.04m².
To find the total number of tiles needed, we divide the floor area (300m²) by the area of one tile (0.04m²): 300m² / 0.04m² = 7,500 tiles.
Since each box contains 50 tiles, we divide the total number of tiles (7,500) by the number of tiles per box (50): 7,500 / 50 = 150 boxes.
To calculate the cost of tiling the floor, we multiply the number of boxes (150) by the cost per box (N$50): 150 boxes x N$50 = N$7,500.
4. Cost of providing air conditioning:
To find the volume of the classroom, we multiply the length, width, and height: 20m x 15m x 5m = 1,500m³.
To calculate the cost of providing air conditioning, we multiply the volume (1,500m³) by the cost per cubic meter (N$60): 1,500m³ x N$60 = N$90,000.
Therefore, the answers to the questions are:
1. The cost of painting the ceiling is N$1,950.
2. The cost of painting the walls (excluding windows and door) is N$2,975.
3. The cost of tiling the floor is N$7,500.
4. The cost of providing air conditioning is N$90,000.