Question

Jack and Jill take out a housing loan to purchase a home worth $480,000. They had a deposit of $80,000. The loan is to be repaid in equal monthly instalments over a term of 20 years. The interest rate quoted by the bank is 8.75%pa nominal with interest added monthly.

(a) How much are the monthly repayments?
(b) How much interest is in the 50th repayment?
(c) If Jack and Jill decide to pay out the loan immediately before making the 100th payment, what is the payout figure? Clearly state any assumptions you make.

Answer 1

To calculate the monthly repayment for the housing loan, we use the loan amount, monthly interest rate, and number of payments in a formula. In this case, the monthly repayment is approximately $3,155.13.

Step-by-step explanation:

To calculate the monthly repayment for the housing loan, we first need to calculate the loan amount. The loan amount is the purchase price of the home minus the deposit. In this case, the loan amount is $480,000 - $80,000 = $400,000.

Next, we can use the formula for calculating the monthly repayment for a loan:

Monthly Repayment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

The monthly interest rate can be calculated by dividing the nominal interest rate by 12 (since interest is added monthly). In this case, the monthly interest rate is (8.75% / 100) / 12 = 0.0073.

Plugging in the values into the formula, we get:

Monthly Repayment = ($400,000 * 0.0073) / (1 - (1 + 0.0073)^(-240))

Using a calculator, we can evaluate this expression to find that the monthly repayment is approximately $3,155.13.