Question

In a new housing development project, the houses are selling for \( \$ 380,000 \) and require a \( 20 \% \) down payment. The buyer is given a choice of 30 -year financing at \( 3.20 \% / y \) year or

Answer 1

The buyer should choose the \(30\)-year financing at \(3.20\%\) per year.

Step-by-step explanation:

In deciding between the two financing options, the key factors to consider are the total cost of the loan and the monthly payments. The total cost of the loan can be calculated using the formula for the total repayment of a loan:

`\[Total\:Repayment = Loan\:Amount + Total\:Interest\]`

For a \(380,000\) house with a \(20\%\) down payment, the loan amount is \(380,000 - 0.20 \times 380,000 = 304,000\). Now, let's calculate the total interest for both financing options:

1. For the \(30\)-year financing at \(3.20\%\) per year, the total interest can be calculated using the formula:

`\[Total\:Interest = Loan\:Amount * Annual\:Interest\:Rate * Loan\:Term\]`

Substituting in the values:

`\[Total\:Interest = 304,000 * 0.032 * 30\]`

2. For the alternative option, the total interest is calculated similarly.

Now, compare the total repayment for both options. The one with the lower total repayment is the more cost-effective choice. Additionally, consider the monthly payments to ensure they are manageable for the buyer.

In this case, despite the lower interest rate for the alternative option, the longer loan term results in a higher total repayment. Therefore, the
`\[Total\:Interest = 304,000 * 0.032 * 30\]` -year financing at \(3.20\%\) per year is the more favorable choice for the buyer.