Daniel and Jan agreed to pay $553,000 for a four-bedroom colonial home in Waltham, Massachusetts, with a $70,000 down payment. They have a 30-year mortgage at a fixed rate of 6.00%. (Use Table 15.1)
a. How much is their monthly payment? (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
To determine their monthly payment, we can use the amortization formula:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value (loan amount)
n = total number of payments
First, we need to calculate the monthly interest rate and the total number of payments.
The monthly interest rate (r) is calculated by dividing the annual interest rate (6.00%) by 12 (months in a year):
r = 6.00% / 12 = 0.06 / 12 = 0.005
The total number of payments (n) is calculated by multiplying the number of years (30) by 12 (months in a year):
n = 30 * 12 = 360
Next, we can substitute the values into the formula:
P = (0.005 * 483,000) / (1 - (1 + 0.005)^(-360))
P = (2,415) / (1 - (1 + 0.005)^(-360))
P = (2,415) / (1 - 0.472167632)
P = (2,415) / (0.527832368)
P ≈ $4,583.07
Therefore, their monthly payment is approximately $4,583.07.