Question

You have decided that you would like to purchase your first house. Given the following information, what will be your fortnightly payments on the home loan to purchase the house (a fortnight is two weeks, and assume there are exactly 26 fortnights in a year).  

You estimate you will need $1,250,000 to purchase the house; ·        You have a deposit of $250,000 which you will use to purchase the house; ·        Your payments on the home loan will commence exactly 1 fortnight from today, ·        The loan term is for exactly 25 years; and, ·        Interest is payable at a fixed rate of 4.25% p.a. compounded weekly (assume there are exactly 52 weeks in a year).​

Answer 1

To calculate the fortnightly payments on the home loan, we need to use the formula for calculating repayments on a loan:

Repayment = (P x r) / (1 - (1 + r)^(-n))

Where:

P = loan principal (amount borrowed)

r = interest rate per fortnight

n = total number of fortnights in the loan term

First, we need to calculate the loan principal:

Loan principal = $1,250,000 - $250,000 = $1,000,000

Next, we need to calculate the interest rate per fortnight. We can convert the annual interest rate to a fortnightly rate as follows:

Fortnightly interest rate = (1 + annual interest rate)^(1/26) - 1

Fortnightly interest rate = (1 + 0.0425)^(1/26) - 1

Fortnightly interest rate = 0.001604 or 0.1604%

Now, we need to calculate the total number of fortnights in the loan term:

Total number of fortnights = 25 years x 26 fortnights per year = 650 fortnights

Finally, we can calculate the fortnightly repayment:

Repayment = ($1,000,000 x 0.001604) / (1 - (1 + 0.001604)^(-650))

Repayment = $5,516.29

Therefore, your fortnightly payments on the home loan to purchase the house will be $5,516.29