Use PMT = [tex]$\frac{P(\frac{r}{n})}{\left[1-(1+\frac{r}{n})^{-nt}\right]}$[/tex] to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $174,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 10%. Complete parts (a) through (e) below.
c. How much must be paid for the three points at closing?
d. Find the monthly payment (excluding escrowed taxes and insurance).
e. Find the total cost of interest over 30 years.
Answer (2)
Calculate the down payment: Down payment = 0.20 × $174 , 000 = $34 , 800 .
Calculate the loan amount: Loan amount = $174 , 000 − $34 , 800 = $139 , 200 .
Calculate the total amount paid: Total paid = $1222 × ( 30 × 12 ) = $439 , 920 .
Calculate the total interest: Total interest = $439 , 920 − $139 , 200 = $300 , 720 .
Explanation
Understanding the Problem We are asked to find the total cost of interest over 30 years for a home loan. We know the price of the home, the down payment percentage, the monthly payment, and the loan term.
Calculating the Loan Amount First, we need to calculate the loan amount. The price of the home is $174 , 000 and the down payment is 20% of the home price. So, the down payment is: Down payment = 0.20 × $174 , 000 = $34 , 800 The loan amount is the price of the home minus the down payment: Loan amount = $174 , 000 − $34 , 800 = $139 , 200
Calculating the Total Amount Paid Next, we calculate the total amount paid over the 30-year loan term. The monthly payment is $1222 , and the loan term is 30 years, which is 30 × 12 = 360 months. So, the total amount paid is: Total paid = $1222 × 360 = $439 , 920
Calculating the Total Interest Paid Finally, we calculate the total cost of interest by subtracting the loan amount from the total amount paid: Total interest = Total paid − Loan amount = $439 , 920 − $139 , 200 = $300 , 720
Final Answer Therefore, the total cost of interest over 30 years is $300 , 720 .
Examples
Understanding the total interest paid on a loan is crucial for financial planning. For example, when purchasing a car or a home, knowing the total interest helps you compare different loan offers and understand the long-term cost. This knowledge enables informed decisions about affordability and the true cost of borrowing, ensuring you choose the most financially sound option.
The payment for the three points at closing is $4,176. The monthly payment for the mortgage is approximately $1,203, and the total interest paid over 30 years amounts to approximately $293,880.
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