The price of a condominium is $179,000. The bank requires a 5% down payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortgage at 6.5%. Use the following formula to determine the regular payment amount.
[tex]PMT=\frac{P(\frac{r}{n})}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}[/tex]
d. Find the monthly payment (excluding escrowed taxes and insurance).
e. Find the total cost of interest over 30 years.
Answer (2)
Calculate the total amount paid: 1075 × 360 = 387000 .
Calculate the down payment: 0.05 × 179000 = 8950 .
Calculate the loan amount: 179000 − 8950 = 170050 .
Calculate the total interest paid: 387000 − 170050 = 216950 . The total cost of interest is 216950 .
Explanation
Understanding the Problem We are asked to find the total cost of interest paid over 30 years for a condominium loan. We know the price of the condominium, the down payment percentage, the monthly payment, and the loan term.
Calculating Total Amount Paid First, we need to calculate the total amount paid over the 30-year period. This is done by multiplying the monthly payment by the total number of months in 30 years. The monthly payment is given as 1075. T h e n u mb ero f m o n t h s i s 30 ye a rs ∗ 12 m o n t h s / ye a r = 360 m o n t h s . T h ere f ore , t h e t o t a l am o u n tp ai d i s : 1075 × 360 = 387000 $
Calculating the Loan Amount Next, we need to calculate the loan amount. This is the price of the condominium minus the down payment. The condominium price is 179 , 000 , an d t h e d o w n p a y m e n t i s 5 0.05 × 179000 = 8950 T h e l o anam o u n t i s t h e n : 179000 − 8950 = 170050 $
Calculating Total Interest Paid Finally, we calculate the total interest paid by subtracting the loan amount from the total amount paid: 387000 − 170050 = 216950
Final Answer Therefore, the total cost of interest over 30 years is $216 , 950 .
Examples
Understanding the total interest paid on a loan is crucial in financial planning. For example, when purchasing a car or a home, knowing the total interest helps you compare different loan options and understand the long-term cost. This calculation allows you to make informed decisions about which loan best fits your budget and financial goals, ensuring you're not caught off guard by the overall expense.
The monthly payment for the condominium is approximately $940.11, and the total cost of interest over 30 years is approximately $168,789.60.
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