Consider a home mortgage of $139855 with a fixed APR of 4.7% for 20 years . Calculate the monthly payment. When the loan is paid off how much will have been paid in total . What percentage of the total payment is interest.

Step 1: To calculate the monthly payment, we can use the formula for the monthly payment on a fixed-rate mortgage:

P = \dfrac{Pv \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}

where:
- P = monthly payment
- Pv = present value of the loan ($139,855)
- r = monthly interest rate ( \dfrac{4.7\%}{12} )
- n = total number of payments (20 years = 240 months)

Step 2: Plugging in the values into the formula:

P = \dfrac{139855 \times \dfrac{0.047}{12} \times (1 + \dfrac{0.047}{12})^{240}}{(1 + \dfrac{0.047}{12})^{240} - 1}

Step 3: Calculating the monthly payment:

P ≈ \dfrac{139855 \times 0.00391667 \times (1.00391667)^{240}}{(1.00391667)^{240} - 1}

Step 4: Calculate the monthly payment.

P ≈ \dfrac{548.89}{0.16903}

P≈\$899.96

Answer: The monthly payment will be approximately $899.96

Step 5: To calculate the total amount paid over 20 years, we can multiply the monthly payment by the total number of payments:

Total \ amount \ paid = P \times n

Totalamountpaid=\$899.96\times240

Totalamountpaid=\$215990.75

Answer: The total amount paid over 20 years will be $215990.75

Step 6: To calculate the percentage of the total payment that is interest, we can subtract the initial loan amount ($215990.75) from the total amount paid and then divide by the total amount paid:

Interest \ percentage = \dfrac{Total \ amount \ paid - Pv}{Total \ amount \ paid} \times 100\%

Interest \ percentage = \dfrac{197191.20 - 139855}{197191.20} \times 100\%

Interestpercentage\approx\frac{215990.75-139855}{215990.75}\times100\%

Interestpercentage≈35.25\%

Answer: The percentage of the total payment that is interest is approximately 35.25%.