Question

Island News purchased a piece of property for $1.79 million. The firm paid a down payment of 20 percent in cash and financed the balance. The loan terms require monthly payments for 20 years at an APR of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?

Answer 1

Answer:

      $\large\boxed{\large\boxed{\ 9,253.92}}$

Explanation:

The conditions of the mortgage are:

• Loan: $ 1.79 million less down payment

                  = $1,790,000 - 20% × $1,790,000 = $1,432,000

• number of payments = 20years × 12 payment/year = 240

• monthly interest = APR/12 = 4.75% / 12 = 0.0475/12 ≈ 0.003958

The amount of each mortgage payment is calculated with this equation:

     $Monthly\text{ }payment=Loan\times \bigg[\dfrac{r(1+r)^t}{(1+r)^t-1}\bigg]$

Substituting the conditions for this mortgage:

$Monthly\text{ }payment=\ 1,432,000\times \bigg[\dfrac{(0.0475/12)(1+(0.0475/12))^{240}}{(1+(0.0475/12))^{240}-1}\bigg]=\ 9,253.92$