Find the monthly payment for the loan. (Round your answer to the nearest cent.)
A $128,000 home bought with a 20% down payment and the balance financed for 30 years at 8.5%
128,000 * .8 = 102,400 principal p
pmt = p [r/{ 1 -(1+r)^-n} ]
n = 30 * 12 = 360
r = .085/12 = .00708333
1 + r = 1.00708333
(1 + r)^-360 = .07878669
1 - (1+r)^-360 = .9212133
.08 / .9212133 = .007689
times principal = $787.37
To find the monthly payment for the loan, we can use the formula for calculating a mortgage payment.
The formula for calculating the monthly mortgage payment is:
M = P [ r(1+r)^n ] / [ (1+r)^n – 1 ]
Where:
M = monthly mortgage payment
P = principal amount (balance financed)
r = monthly interest rate (annual interest rate divided by 12 and expressed as a decimal)
n = total number of monthly payments
First, let's calculate the principal amount or balance financed. The home was bought with a 20% down payment, so the principal amount is 80% of the home's value:
Principal amount = 80% of $128,000 = 0.80 * $128,000 = $102,400
Next, let's calculate the monthly interest rate. The annual interest rate is 8.5%, so the monthly interest rate is:
Monthly interest rate = 8.5% / 12 = 0.085 / 12 = 0.0070833
Now, let's calculate the total number of monthly payments. The loan term is 30 years, which means 30 * 12 = 360 monthly payments.
Total number of monthly payments = 30 years * 12 months/year = 360 payments
Plugging these values into the mortgage payment formula, we get:
M = $102,400 [ 0.0070833(1+0.0070833)^360 ] / [ (1+0.0070833)^360 – 1 ]
Evaluating this expression using a calculator, we find:
M ≈ $795.73
Therefore, the monthly payment for the loan is approximately $795.73.