Final answer:
The monthly payment for the condo listed at $1.4 million with a 20% down payment and 5% interest rate for 30 years is calculated by determining the loan amount after the down payment, and then using the mortgage payment formula involving the loan principal, monthly interest rate, and number of payments.
Step-by-step explanation:
The calculation for the monthly payment of a condo in Orange Beach, Alabama, listed for $1.4 million with a 20% down payment and financing at a 5% interest rate for 30 years is done using the formula for a fixed-rate mortgage.
To begin, we must determine the loan amount by subtracting the down payment from the total cost of the condo. The down payment is 20% of $1.4 million, which is $280,000. Therefore, the loan amount is $1.4 million minus $280,000, resulting in $1,120,000.
Using the loan amount, the formula for a fixed-rate mortgage payment, and the given interest rate and time frame, we can calculate the monthly payment. The monthly interest rate is 5% per year, which is 0.05/12 = 0.004167 per month. The total number of payments over 30 years is 30 * 12 = 360. The formula for the monthly payment is M = P[i(1+i)^n] / [(1+i)^n - 1], where M is the monthly payment, P is the principal amount (loan amount), i is the monthly interest rate, and n is the number of payments.
Using the values we have:
M = $1,120,000[0.004167(1+0.004167)^360] / [(1+0.004167)^360 - 1]
Calculating this gives us the monthly payment, which is closest to one of the given multiple-choice options.