A couple purchases a house for $400,000.00. They pay 20% down at closing, and take out a mortgage of $320,000.00. The mortgage company offers them a 4.80% annual rate with monthly compounding. The mortgage will require monthly payments for the next 30 years.
What will be the monthly payment on this mortgage?
Answer:
$ 1678.91
Explanation:
Given that;
Cost of purchasing a house = $400,000.00
Down payment =20%
Mortgage Value (MV) = $320,000.00
Annual rate offered by the mortgage company = 4.80% yearly i.e 0.4 per month
Duration of the Mortgage Loan (n) = 30 years which is equivalent to 360 months.
if we represent the monthly repayment with MR ,To calculate the monthly repayment MR;we have;
MV = MR × [tex](\frac{1}{i})*[1-(\frac{1}{(1+i)^{n}} )}][/tex]
where i = 0.004 (4.8 % annually expressed as 0.48, divided by 12 monthly payments per year)
∴
[tex]320,000.00[/tex] = [tex]MR[/tex] [tex]*(\frac{1}{0.004})*[1-(\frac{1}{1+0.004)^{360}}})][/tex]
320,000.00 = MR × 190.60
Monthly repayment (MR) = $ 1678.90870933
Monthly repayment (MR) ≅ $ 1678.91
