Question

You want to buy a house that costs \$320,000. You will make a down payment equal...

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