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arsen [322]
4 years ago
9

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 c

ompany offers them a 4.80% annual rate with monthly compounding. The mortgage will require monthly payments for the next 30 years.
Chemistry
1 answer:
11Alexandr11 [23.1K]4 years ago
5 0

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 × (\frac{1}{i})*[1-(\frac{1}{(1+i)^{n}} )}]

where i = 0.004 (4.8 % annually expressed as 0.48, divided by 12 monthly payments per year)

∴

320,000.00 = MR *(\frac{1}{0.004})*[1-(\frac{1}{1+0.004)^{360}}})]

320,000.00 = MR × 190.60

Monthly repayment (MR) = $ 1678.90870933

Monthly repayment (MR) ≅ $ 1678.91

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