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. Complete parts (a) through (e) below.
[tex]PMT=\frac{P(\frac{r}{n})}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}[/tex]
a. Find the down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
Answer (1)
One point equals 1% of the mortgage amount.
Calculate 1% of the mortgage amount: 170050 × 0.01 = 1700.5 .
Round the result to the nearest dollar: 1700.5 ≈ 1701 .
The cost of one point at closing is 1701 .
Explanation
Understanding the problem The problem states that one point is paid at the time of closing. One point is equal to 1% of the mortgage amount. We are given that the mortgage amount is $170,050.
Calculating one point To find the cost of one point, we need to calculate 1% of the mortgage amount, which is $170,050. To do this, we multiply the mortgage amount by 0.01.
Calculating the cost The cost of one point is calculated as follows: 170050 × 0.01 = 1700.5 Since we need to round to the nearest dollar, we round $1700.5 to $1701.
Final Answer Therefore, the amount that must be paid for the one point at closing is $1701.
Examples
Understanding points in mortgages is crucial in real estate. For example, if you're buying a house and have the option to pay points to lower your interest rate, knowing how to calculate the cost of those points helps you determine if it's a worthwhile investment. Each point costs 1% of your mortgage. So, on a mortgage of $200 , 000 , one point would cost $2 , 000 . Paying points can reduce your monthly payments, but you need to calculate whether the upfront cost saves you more money over the life of the loan.
