You want to buy a house that costs $320,000. You will make a down payment equal to 20 percent of the price of the house and finance the remainder with a loan that has an interest rate of 4.55 percent compounded monthly. If the loan is for 30 years, what are your monthly mortgage payments?
Given
House Cost = $ 320000
Down payment = 20% ( Purchase price )
= $ 320000*20%
= $ 64000
Loan amount = 80% ( Purchase price )
= $ 320000*80%
= $ 256000
Interest rate = 4.55% Compounded Monthly
Interest rate per month = 4.55% /12 = 0.379167%
Time period = 30 Years
No.of Monthly payment s= 30*12= 360
We know that
Present value of the loan payments is equal to the loan amount.
Present value of Ordinary Annuity= C [ { 1-( 1+i)^-n} /i]
Here C = Cash flow per period
I =Interest rate per period
n = No.of payments
$ 256000= C [ { 1-( 1+0.003792)^-360} /0.003792]
$ 256000= C [ { 1-( 1.003792)^-360}/0.003792]
$ 256000= C [ { 1-0.256041} /0.003792]
$ 256000= C [ {0.743959/0.003792]
$ 256000= C *$ 196.1918
$ 256000/ $ 196.1918 = C
C = $ 1304.846
Hence the Monthly Mortgage payment is $ 1304.846
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