The price of a home is $320,000. The bank requires an 8% down payment and three points

at the time of closing. The cost of the home is financed with a 30-year fixed rate at 6%.
Find the amount that must be paid for the three points at closing & Find the monthly payment.

Given:

purchase price = 320,000
down payment = 8%
mortgage bought down (to 6%) with 3 points (3%).
Term, n= 30 years
rate, i=6% per annum = 6%/12 = 0.005
compounding frequency = monthly (ASSUMED).

Solution:
Down payment = 8% * 320,000 = 25,600
Loan, P = 320,000 - 25,600 = 294,400
Cost of 3 points = 3% * 294,400 = 8832 (amount to be paid at closing)

Monthly payment = Pi(1+i)^(12n)/((1+i)^(12n)-1)
=294400*0.005*(1.005^(12*30))/(1.005^(12*30)-1)
=1765.0767
=1765.08 (to the nearest cent).

what problem can solved by using GCF.

To find the amount that must be paid for the three points at closing, we first need to determine the value of three points as a percentage of the loan amount.

1 point is equal to 1% of the loan amount. So, three points would be equal to 3% of the loan amount.

The loan amount can be calculated by subtracting the down payment from the price of the home. So, to find the loan amount, we need to calculate 8% of the price of the home and subtract it from the price:

Down payment = 8% of $320,000 = 0.08 * $320,000 = $25,600
Loan amount = $320,000 - $25,600 = $294,400

Now, we can find the amount that must be paid for the three points at closing:

Three points = 3% of $294,400 = 0.03 * $294,400 = $8,832

Therefore, the amount that must be paid for the three points at closing is $8,832.

To find the monthly payment, we can use the loan amount, the interest rate, and the loan term. We can use the following formula to calculate the monthly payment for a fixed-rate mortgage:

Monthly payment = [Loan amount * (Interest rate / 12)] / (1 - (1 + Interest rate / 12)^(-number of months))

In this case, the loan amount is $294,400, the interest rate is 6% (expressed as a decimal, 0.06), and the loan term is 30 years (which corresponds to 360 months).

Plugging in these values, we get:

Monthly payment = [$294,400 * (0.06 / 12)] / (1 - (1 + 0.06 / 12)^(-360))

Calculating this expression will give us the monthly payment.