You wish to purchase a house for $200,000 with 20% down. You will have it financed over 30 years at a rate of 8%. In addition, your yearly real estate tax is $4,800 while your monthly insurance payment on the home will be $30. What is your monthly mortgage payment? How much does your house cost per month including principal, interest, real estate taxes, and insurance?
first find the mortgage payment, without the taxes and insurance.
200000 less 20 down leaves 160000
let the payment be P
i = .08/12 = .00666666...
n = 12(30) = 360
160000 = P( 1- 1.006666667^-360)/.00666667
160000 = P(136.2835045)
p = 1174.02
I will let you finish it.
910
To calculate your monthly mortgage payment, we need to determine the loan amount and monthly interest rate.
Loan amount on a $200,000 house with a 20% down payment would be:
Loan amount = $200,000 - (20% x $200,000)
Loan amount = $200,000 - $40,000
Loan amount = $160,000
To calculate the monthly interest rate, we divide the annual interest rate by 12:
Monthly interest rate = 8% / 12
Monthly interest rate = 0.08 / 12
Monthly interest rate = 0.0067
Next, we can calculate the monthly mortgage payment using the loan amount, loan term, and monthly interest rate using the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly mortgage payment
P = Loan amount
i = Monthly interest rate
n = Loan term in months
M = $160,000 [ 0.0067(1 + 0.0067)^360 ] / [ (1 + 0.0067)^360 - 1 ]
M = $1,138.61 (rounded to the nearest cent)
So, your monthly mortgage payment is approximately $1,138.61.
To determine the total monthly cost of the house, we need to consider the principal and interest (mortgage payment), real estate taxes, and insurance.
Principal and Interest: $1,138.61 (as calculated above)
Real Estate Taxes: $4,800 / 12 = $400
Insurance: $30
Total monthly cost = Principal and Interest + Real Estate Taxes + Insurance
Total monthly cost = $1,138.61 + $400 + $30
Total monthly cost = $1,568.61
Therefore, the house costs approximately $1,568.61 per month, including principal, interest, real estate taxes, and insurance.
To calculate the monthly mortgage payment, we first need to find the loan amount, and then calculate the monthly payment using the loan amount, interest rate, and loan term.
1. Loan amount:
To find the loan amount, multiply the purchase price of the house by the down payment percentage:
Loan amount = Purchase price x Down payment percentage
Given:
Purchase price = $200,000
Down payment percentage = 20% = 0.20
Loan amount = $200,000 x 0.20 = $40,000
2. Monthly mortgage payment:
To calculate the monthly mortgage payment, we use the formula for calculating the monthly payment on a fixed-rate mortgage:
M = P * (r*(1+r)^n)/((1+r)^n-1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate (Annual interest rate / 12)
n = Total number of payments (Loan term in years * 12)
Given:
P = $40,000 (Loan amount)
Annual interest rate = 8%
Loan term = 30 years
r = (8% / 100) / 12 = 0.0067 (approximately)
n = 30 * 12 = 360 (total number of payments)
Using the formula:
M = $40,000 * (0.0067*(1+0.0067)^360)/((1+0.0067)^360-1)
M ≈ $293.34
Therefore, the monthly mortgage payment is approximately $293.34.
3. Including real estate taxes and insurance:
To calculate the total monthly cost of the house, including principal, interest, real estate taxes, and insurance, we add the monthly mortgage payment, annual real estate tax divided by 12, and the monthly insurance payment:
Total Monthly Cost = Monthly mortgage payment + (Annual real estate tax / 12) + Monthly insurance payment
Given:
Annual real estate tax = $4,800
Monthly insurance payment = $30
Total Monthly Cost = $293.34 + ($4,800/12) + $30
Total Monthly Cost = $293.34 + $400 + $30
Total Monthly Cost = $723.34
Therefore, the total monthly cost of the house, including principal, interest, real estate taxes, and insurance, is $723.34.