A condo is advertised in The Wall Street Journal for $350,000. It states in the ad that a 20% down payment is required. The rate of interest is 11% on a 25-year mortgage. What would be (A) the monthly payment along with (B) the total cost of interest
To calculate the monthly payment and the total cost of interest for the condo, we need to use the formula for a fixed-rate mortgage.
First, let's calculate the down payment. The ad states that a 20% down payment is required for a $350,000 condo. So, we multiply $350,000 by 20% (or 0.2) to find the down payment amount:
Down payment = $350,000 * 0.2 = $70,000
Now, we need to determine the loan amount, which is the purchase price of the condo minus the down payment:
Loan amount = $350,000 - $70,000 = $280,000
To calculate the monthly payment, we can use the following formula:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
M = Monthly payment
P = Loan amount
i = Monthly interest rate
n = Number of payments (in months)
Let's break down the components and calculate them:
Monthly interest rate (i) = Annual interest rate / (12 * 100)
Given the annual interest rate is 11%, the monthly interest rate is:
Monthly interest rate (i) = 11% / (12 * 100) = 0.00917
Number of payments (n) = Loan term in years * 12
Given the loan term is 25 years, the number of payments is:
Number of payments (n) = 25 * 12 = 300
Now, let's calculate the monthly payment (M):
M = $280,000 [0.00917(1 + 0.00917)^300] / [(1 + 0.00917)^300 - 1]
Using a calculator or spreadsheet, the monthly payment (M) is approximately $2,687.69.
To calculate the total cost of interest, multiply the monthly payment by the number of payments and subtract the loan amount:
Total cost of interest = (M * n) - P
Total cost of interest = ($2,687.69 * 300) - $280,000
Using a calculator or spreadsheet, the total cost of interest is approximately $506,307.31.
So, the answer to (A) is that the monthly payment for this mortgage would be approximately $2,687.69, and the answer to (B) is that the total cost of interest over the 25-year mortgage would be approximately $506,307.31.