Question

Use PMT= (n) + -nt to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $139,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Complete parts (a) through (e) below.​

Answer 1

To determine the regular payment amount for a house loan, use the formula PMT = (n) + -nt. Calculate the loan amount after the down payment, then determine the number of payments, the regular payment amount is $1300.

Step-by-step explanation:

To determine the regular payment amount for a house loan, we can use the formula PMT = (n) + -nt. In this formula, n represents the number of payments and t represents the interest rate per period.

First, we need to calculate the loan amount after the down payment and points. The price of the home is $139,000, and the down payment is 20%, so the loan amount is $139,000 - $139,000 x 0.2 = $111,200.

Next, we calculate the number of payments. Since the loan is a 30-year fixed-rate mortgage, there will be 30 x 12 = 360 payments.

Finally, we can calculate the regular payment amount using the formula PMT = (n) + -nt. Plugging in the values, we have PMT = (360) + -360 x 0.085 = $1300.20.

Rounding this to the nearest dollar, the regular payment amount is $1300.

Answer 2

The regular payment amount, rounded to the nearest dollar, is approximately $855.

How did we get the value?

The standard formula to calculate the monthly payment (PMT) for a fixed-rate mortgage is:

`\[ PMT = P * (r(1+r)^n)/((1+r)^n - 1) \]`

where:

-
`\(P\)` is the principal amount (loan amount),

-
`\(r\)` is the monthly interest rate (annual interest rate divided by 12 and expressed as a decimal),

-
`\(n\)` is the number of payments (loan term in years multiplied by 12).

Let's calculate the monthly payment amount:

(a) Calculate the Down Payment:

`\[ \text{Down Payment} = 0.20 * \$139,000 = \$27,800 \]`

(b) Calculate the Loan Amount (Principal):

`\[ \text{Loan Amount} = \$139,000 - \$27,800 = \$111,200 \]`

(c) Calculate the Loan Term in Months (n):

`\[ n = 30 * 12 = 360 \]`

(d) Calculate the Monthly Interest Rate (r):

`\[ r = (0.085)/(12) \]`

Let's calculate the monthly interest rate:

`\[ r = (0.085)/(12) \approx 0.0070833 \]`

(e) Use the Formula to Calculate Monthly Payment (PMT):

`\[ PMT = (\$111,200 * 0.0070833 * (1+0.0070833)^(360))/((1+0.0070833)^(360) - 1) \]`

Calculating this expression will give you the monthly payment amount. Rounding to the nearest dollar, the result is:

`\[ PMT \approx \$855 \]`

So, the regular payment amount, rounded to the nearest dollar, is approximately $855.