The Chavara family buys a house for $225,000. They pay $50,000 down and take out a 30-year mortgage on the balance. Find their monthly payment and the total amount of interest they will pay if the interest rate is 6%.
I will assume the rate is 6% per annum compounded monthly
i = .06/12 = .005
n = 30x12 = 360
outstanding balance = 225000-50000 = 175000
let the payment be P
175000 = P[ 1 - 1.005^-360 ]/.005
solve for P
(I got 1049.21)
To find the monthly payment and the total interest amount paid, we can use the formula for calculating the monthly payment of a mortgage:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan amount (balance after down payment)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of payments (30 years multiplied by 12 months)
Step 1: Calculate the loan amount (balance after down payment):
Loan amount = Total house price - Down payment
Loan amount = $225,000 - $50,000
Loan amount = $175,000
Step 2: Calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 6% / 12
Monthly interest rate = 0.06 / 12
Monthly interest rate = 0.005
Step 3: Calculate the total number of payments:
Total number of payments = Number of years * 12
Total number of payments = 30 * 12
Total number of payments = 360
Step 4: Substitute the values into the formula and calculate the monthly payment:
M = $175,000 * (0.005 * (1 + 0.005)^360) / ((1 + 0.005)^360 - 1)
Using a calculator or spreadsheet, the monthly payment comes out to be approximately $1,049.34.
Step 5: Calculate the total amount of interest paid:
Total interest paid = (Monthly payment * Total number of payments) - Loan amount
Total interest paid = ($1,049.34 * 360) - $175,000
Using a calculator or spreadsheet, the total interest paid comes out to be approximately $138,562.31.
Therefore, the Chavara family's monthly payment is approximately $1,049.34 and the total interest they will pay is approximately $138,562.31.