Question

a borrower takes out a 30-year mortgage loan for $250,000 with an interest rate of 5 percent and monthly payments. what portion of the first month's payment would be applied to interest

Answer 1

The interest portion in the first payment is 1041.65 dollars which are calculated by multiplying 250,000 dollars by 0.0041666 rate of interest and the percentage of interest portion is equal to 77.62%.

What is a mortgage loan?

A loan mortgage is a secured mortgage that lets you avail finances through imparting an immovable asset, which includes a residence or business property, as collateral to the lender. The lender continues the asset till you pay off the mortgage.

here, the given information -

Monthly payment formula of the mortgage loan:

$Monthly loan payment = P \times\, r\, \times \frac{(1+r)^{n} }{(1+r)^{n} - 1 }$

P: Principal = $250,000

r is rate= 5%, as it is paid monthly, therefore 5/12% - 0.41666%

n = 30*12 - 360months

$\rm\, Monthly \,loan \,payment = 250,000 \times\, 0.0041666\, \times \frac{(1+0.0041666)^{360} }{(1+0.0041666)^{360} - 1 }\\\\Monthly \,loan \,payment = 1041.65 \times \frac{(1.0041666)^{360} }{(1.0041666)^{360} -1 } \\\\Monthly \,loan \,payment = 1041.65 \times \frac{4.4676}{4.4676 - 1} \\\rm\,\\Monthly \,loan \,payment = \ 1342.05$

Now, the interest portion in the first payment is 0.0041666 * 250,000 = $1041.65

Percentage of interest portion in the first monthly payment:

$\rm\, Percentage \,of \,interest\, portion = \frac{1041.65}{1342.05} \\\\\rm\, Percentage \,of \,interest\, portion = 77.62\%$

Thus, the interest portion in the first payment is 1041.65 dollars which is calculated by multiplying 250,000 dollars by 0.0041666 rate of interest and the percentage of interest portion is equal to 77.62%.

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