Question 6 of 15, Step 1 of 1 Manuel purchases a house and gets a 30 -year mortgage for $$ \$ 140,000 $$ at $$ 4.75 \% $$ APR. In addition to the monthly payment, the lender requires him to pay into an escrow account for the homeowners insurance and property tax. His homeowners insurance is $$ \$ 1000 $$ per year and the property tax is $$ \$ 1400 $$ per year, Determine the monthly payment to the lender that includes the insurance and property tax. Round your answer to the nearest cent. Formulas $$ \begin{array}{l} ext { Regular Payment for Fixed } \ ext { Installment Loans } \ ext { Number of Fixed Payments } \ ext { Required to Pay Off Credit Card } \ ext { Debt }\end{array} \quad \mathrm{R}=\frac{-\log \left[1-\frac{\mathrm{r}}{\mathrm{n}}\left(\frac{\mathrm{A}}{\mathrm{PMT}} ight) ight]}{\log \left(1+\frac{\mathrm{r}}{\mathrm{n}} ight)} $$ Answer

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Question 6 of 15, Step 1 of 1 Manuel purchases a house and gets a 30 -year mortgage for $$ \$ 140,000 $$ at $$ 4.75 \% $$ APR. In addition to the monthly payment, the lender requires him to pay into an escrow account for the homeowners insurance and property tax. His homeowners insurance is $$ \$ 1000 $$ per year and the property tax is $$ \$ 1400 $$ per year, Determine the monthly payment to the lender that includes the insurance and property tax. Round your answer to the nearest cent. Formulas $$ \begin{array}{l}	ext { Regular Payment for Fixed } \ 	ext { Installment Loans } \ 	ext { Number of Fixed Payments } \ 	ext { Required to Pay Off Credit Card } \ 	ext { Debt }\end{array} \quad \mathrm{R}=\frac{-\log \left[1-\frac{\mathrm{r}}{\mathrm{n}}\left(\frac{\mathrm{A}}{\mathrm{PMT}}ight)ight]}{\log \left(1+\frac{\mathrm{r}}{\mathrm{n}}ight)} $$ Answer

UpStudy AI · Accepted Answer

Step 1. Compute the basic monthly mortgage payment using the mortgage formula (also known as the annuity formula):

PMT = P · [r(1 + r)ⁿ] / [(1 + r)ⁿ – 1]

where  
  P = $140,000 (principal)  
  APR = 4.75% → Monthly interest rate r = 0.0475/12 ≈ 0.00395833  
  n = 30 years × 12 = 360 months

First, calculate (1 + r)ⁿ:  
  (1 + 0.00395833)³⁶⁰  
A rough calculation shows this is approximately 4.147.

Now plug into the formula:
  PMT ≈ 140,000 × [0.00395833 × 4.147] / [4.147 – 1]

Multiply in numerator:
  0.00395833 × 4.147 ≈ 0.01641  
  Then, 140,000 × 0.01641 ≈ 2297.4

The denominator is:
  4.147 – 1 = 3.147

Thus,  
  PMT ≈ 2297.4 / 3.147 ≈ 730.06

Step 2. Include the escrow for homeowners insurance and property tax.  
Insurance: $1,000 per year  
Property Tax: $1,400 per year  
Total annual escrow amount = $1,000 + $1,400 = $2,400

The monthly escrow contribution is:  
  $2,400 / 12 = $200

Step 3. Add the escrow to the monthly mortgage payment:
  Total monthly payment ≈ $730.06 + $200 ≈ $930.06

Rounded to the nearest cent, the monthly payment to the lender (including insurance and property tax) is $930.06.
The monthly payment to the lender, including insurance and property tax, is approximately \$930.06.

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