Philani sees the following advert:
SCOOTER FOR SALE
R15 000 CASH
HIRE PURCHASE AGREEMENT
AVAILABLE
Since he cannot afford to pay cash for the scooter, he opts for the hire purchase
agreement which states the following:
15% deposit
24 monthly equal instalments
Interest rate: 10% per annum
3.1.1 How much will his deposit be? (1)
3.1.2 Calculate the total amount that he must still pay. (3)
3.1.3 Calculate the monthly instalments. (2)
To calculate the answers, we'll follow the given information step by step:
3.1.1 How much will his deposit be?
The deposit is 15% of the total price. Since the total price is R15,000, the deposit can be calculated as follows:
Deposit = 15% of R15,000
Deposit = (15/100) * R15,000
Deposit = R2,250
Therefore, Philani's deposit will be R2,250.
3.1.2 Calculate the total amount that he must still pay.
To calculate the total amount that Philani must still pay, we need to subtract the deposit from the total price. The deposit is R2,250, and the total price is R15,000. Thus:
Total amount to pay = Total price - Deposit
Total amount to pay = R15,000 - R2,250
Total amount to pay = R12,750
Therefore, Philani must still pay a total amount of R12,750.
3.1.3 Calculate the monthly instalments.
To calculate the monthly instalments, we'll divide the total amount to pay by the number of months. Philani will make 24 monthly instalments, and the total amount to pay is R12,750. Thus:
Monthly instalments = Total amount to pay / Number of months
Monthly instalments = R12,750 / 24
Monthly instalments ≈ R531.25 (rounded to the nearest cent)
Therefore, Philani's monthly instalments will be approximately R531.25.
3.1.1 The deposit will be R2,250.
3.1.2 The total amount that he must still pay is R12,750.
3.1.3 The monthly instalments will be approximately R531.25.
To calculate the answers to the questions, we can use the information given in the hire purchase agreement.
3.1.1 How much will his deposit be? (1)
The deposit is stated as 15% of the total amount. So, to calculate the deposit, we need to find 15% of the total amount:
Deposit = 15% of R15,000
= (15/100) * R15,000
= R2,250
Therefore, Philani's deposit will be R2,250.
3.1.2 Calculate the total amount that he must still pay. (3)
The total amount to be paid can be calculated by adding the deposit to the remaining amount after the deposit:
Remaining amount = Total amount - Deposit
= R15,000 - R2,250
= R12,750
Therefore, the total amount that Philani must still pay is R12,750.
3.1.3 Calculate the monthly instalments. (2)
The monthly instalments can be calculated by dividing the remaining amount by the number of months, with interest added.
Monthly interest rate = Annual interest rate / 12
= 10% / 12
Monthly instalment amount = (Remaining amount + (Monthly interest rate * Remaining amount)) / Number of months
= (R12,750 + (10% / 12 * R12,750)) / 24
First, let's calculate the monthly interest rate:
Monthly interest rate = 10% / 12
= 0.10 / 12
= 0.008333333
Now, we can calculate the monthly instalment amount:
Monthly instalment amount = (R12,750 + (0.008333333 * R12,750)) / 24
= (R12,750 + R106.25) / 24
= R12,856.25 / 24
= R535.68 (rounded to two decimal places)
Therefore, the monthly instalments for Philani will be approximately R535.68.
To calculate the answers to these questions, we need to follow the guidelines provided in the hire purchase agreement. Let's go step-by-step:
3.1.1 How much will his deposit be? (1)
According to the hire purchase agreement, the deposit is set at 15% of the total cost of the scooter. The advert states that the scooter is being sold for R15,000. Therefore, the deposit will be 15% of R15,000:
Deposit = 15/100 * R15,000 = R2,250
Therefore, Philani's deposit will be R2,250.
3.1.2 Calculate the total amount that he must still pay. (3)
To calculate the total amount Philani must still pay, we subtract the deposit from the total cost of the scooter. The total cost is R15,000 and the deposit is R2,250:
Total Amount to be Paid = R15,000 - R2,250 = R12,750
Therefore, Philani must still pay a total of R12,750.
3.1.3 Calculate the monthly instalments. (2)
To calculate the monthly instalments, we need to consider the total amount to be paid, the duration of the hire purchase agreement, and the interest rate.
The total amount to be paid is R12,750. The hire purchase agreement specifies that the total amount will be paid in 24 monthly instalments.
To calculate the monthly instalments, we need to use the formula for calculating the equal monthly instalments in a hire purchase agreement with compound interest:
Monthly Instalments = (Total Amount to be Paid * Interest Rate * (1 + Interest Rate)^Number of Instalments) / ((1 + Interest Rate)^Number of Instalments - 1)
Using the given values:
Total Amount to be Paid = R12,750
Interest Rate = 10% per annum (convert to decimal by dividing by 100 = 0.10)
Number of Instalments = 24
Now we can calculate the monthly instalments:
Monthly Instalments = (R12,750 * 0.10 * (1 + 0.10)^24) / ((1 + 0.10)^24 - 1)
Calculating this equation will give us the value of the monthly instalments.
Therefore, to find out the exact value for the monthly instalments, you can substitute these values into a calculator or a spreadsheet to get the solution.