The price of a home is $400,000. The mortgage company requires a down payment of 20% and 1 point at the time of closing for a 30-year loan at a rate of 4.25%. The closing costs of $7,500 and the points cannot be included in the loan. Required:
a. Find the down payment.
b. Find the amount financed.
c. How much must be paid at the time of closing?
d. Find the monthly payment.
e. Find the total cost of interest.
f. How much of the principal was repaid in the first payment?

(a) $80,000  (b) $320,000  (c) $10,700  (d) $1,574.21  (e) $246,714.75  (f)  $440.87

Explanation:

Solution

Given that:

Now

(a)The price of the house = 400,000

The down payment = 20%

The value of down payment = 20%*400,000

= $80,000

(b) The loan  value or amount financed = Purchase Price - Down Payment

= 400,000 - 80,000

= $320,000

(c)  Thus

The loan value = $320,000

1 Point has to be paid at the closing time and also, the closing  fees of $7,500 has to be paid

So, the amount paid at the time of closing = 1%*320000 + 7500

= 3200 + 7500

= $10,700

(d) To compute the Monthly payment we make use of the PMT function in Excel

Which is given below:

4= PMT(Rate, Nper, PV, FV,Type)

Rate = 4.25%/12

Nper = 30*12

= 360

PV = 320000

FV = 0

Type = 0

=PMT(4.25%/12, 360, -400000,0,0)

= $1,574.21

(e) Now we find the total amount paid over 30 years  which is given as :

Total amount paid over 30 years

= 1,574.21*360 = $566,714.75

The loan amount = $320,000

Total interest cost = 566,714.75 - 320,000

= $246,714.75

(f)  The Interest paid during first installment is as follows:

= 4.25%*320000/12

= $1,133.33

Monthly installment = $1,574.21

The Principal repayment = Monthly installment - Interest paid during first installment

= 1,574.21 - 1,133.33

= $440.87

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