Joe and Wendy bought a house costing $210000. They paid a 35% deposit and borrowed the remainder at a flat interest rate of 7.75% p.a. payable over 25 years. What is the amount of their total monthly instalment?
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To find the total monthly installment, we need to calculate the remaining loan amount after the deposit and then use the flat interest rate to calculate the monthly payments.
1. Calculate the deposit amount:
Deposit amount = 35% of $210000
Deposit amount = 0.35 * $210000
Deposit amount = $73500
2. Calculate the loan amount:
Loan amount = Total cost - Deposit amount
Loan amount = $210000 - $73500
Loan amount = $136500
3. Calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 7.75% / 12
Monthly interest rate = 0.647%
4. Calculate the number of monthly payments:
Number of monthly payments = Loan duration in years * 12
Number of monthly payments = 25 years * 12
Number of monthly payments = 300
5. Calculate the monthly installment:
Monthly installment = Loan amount * Monthly interest rate * (1 + Monthly interest rate)^Number of monthly payments / ((1 + Monthly interest rate)^Number of monthly payments - 1)
Monthly installment = $136500 * 0.00647 * (1 + 0.00647)^300 / ((1 + 0.00647)^300 - 1)
By substituting the values in the formula and evaluating it, we can find the total monthly installment.
To find the amount of their total monthly installment, we need to calculate two things. First, we need to determine the loan amount they borrowed by subtracting the deposit from the total cost of the house. Then, we can calculate the monthly payment based on the loan amount and the terms of the loan.
Step 1: Calculate the loan amount
The total cost of the house is $210,000. They paid a 35% deposit, which means they paid 35/100 * $210,000 = $73,500 as a deposit.
Therefore, the loan amount is $210,000 - $73,500 = $136,500.
Step 2: Calculate the monthly installment
To calculate the monthly installment, we can use the formula for calculating fixed monthly payments on a loan:
A = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
A = Monthly installment
P = Loan amount
r = Monthly interest rate
n = Total number of payments
Given:
P = $136,500
r = 7.75% p.a. = 7.75%/12 = 0.6458% monthly
n = 25 years * 12 months/year = 300 months
Substituting these values into the formula:
A = $136,500 * 0.006458 * (1 + 0.006458)^300 / ((1 + 0.006458)^300 - 1)
Using a calculator, we can evaluate this expression to find the monthly installment. The result is approximately $936.96.
So, the amount of their total monthly installment is $936.96.