QUESTION 2 2.1 Busi buys a house and takes out a loan for R450 000. The interest rate is 11% p.a., compounded monthly. 2.1.1 Calculate her monthly repayments if the loan is paid over 20 years. (4) 2.1.2 How much does she pay in total over 20 years to repay the loan? (1) 2.1.3 Calculate the balance of the loan after 15 years. (4)
2.1.1 To calculate her monthly repayments, we need to use the formula for monthly payment on a loan:
Monthly payment = (loan amount * monthly interest rate) / (1 - (1 + monthly interest rate)^(-number of months))
First, let's calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = 11% / 12 = 0.11 / 12 = 0.0091666667
Now let's calculate the number of months:
Number of months = 20 years * 12 = 240 months
Now we can plug the values into the formula:
Monthly payment = (450000 * 0.0091666667) / (1 - (1 + 0.0091666667)^(-240))
Using a calculator, the monthly payment is approximately R4,676.82.
2.1.2 To calculate how much she pays in total over 20 years, we can simply multiply the monthly payment by the number of months:
Total payment = Monthly payment * Number of months = R4,676.82 * 240 = R1,122,763.04
So, she pays a total of approximately R1,122,763.04 over 20 years to repay the loan.
2.1.3 To calculate the balance of the loan after 15 years, we need to use the formula for compound interest:
Balance = Principal * (1 + interest rate)^time
Plugging in the values:
Balance = 450000 * (1 + 0.11/12)^(15*12)
Using a calculator, the balance is approximately R83,785.07.
So, the balance of the loan after 15 years is approximately R83,785.07.
Step 1: Calculate the monthly interest rate.
The annual interest rate is given as 11%. To find the monthly interest rate, divide it by 12 (the number of months in a year).
Monthly interest rate = Annual interest rate / 12 = 11% / 12 = 0.00916666667
Step 2: Calculate the number of monthly payments.
The loan is paid over 20 years, so the total number of monthly payments is 20 years * 12 months/year = 240 payments.
Step 3: Calculate the monthly repayment amount using the loan formula.
Monthly repayment amount = Loan amount * (monthly interest rate * (1 + monthly interest rate)^number of payments) / ((1 + monthly interest rate)^number of payments - 1)
Monthly repayment amount = R450,000 * (0.00916666667 * (1 + 0.00916666667)^240) / ((1 + 0.00916666667)^240 - 1) ≈ R4,414.67
Therefore, the monthly repayment amount is approximately R4,414.67.
Step 4: Calculate the total amount paid over 20 years.
To find the total amount paid over 20 years, multiply the monthly repayment amount by the total number of payments.
Total amount paid = Monthly repayment amount * Number of payments = R4,414.67 * 240 = R1,059,520
Therefore, Busi pays a total of R1,059,520 over 20 years to repay the loan.
Step 5: Calculate the balance of the loan after 15 years.
To find the balance of the loan after 15 years, calculate the number of remaining payments and use the loan formula.
Remaining number of payments = Total number of payments - Number of payments made after 15 years
Remaining number of payments = 240 - (15 * 12) = 240 - 180 = 60 payments
Balance of the loan = Loan amount * ((1 + monthly interest rate)^number of payments - (1 + monthly interest rate)^number of payments paid) / ((1 + monthly interest rate)^number of payments - 1)
Balance of the loan = R450,000 * ((1 + 0.00916666667)^240 - (1 + 0.00916666667)^180) / ((1 + 0.00916666667)^240 - 1)
Therefore, the balance of the loan after 15 years is approximately R309,332.36.