Section 10-2: Monthly Payment and Total Interest

To calculate the monthly payment and total interest for a mortgage loan, you can use the formula for calculating the monthly payment of a fixed-rate mortgage:

Where:

• $M$ = Monthly payment
• $P$ = Principal loan amount (the initial loan balance)
• $r$ = Monthly interest rate (annual interest rate divided by 12 and expressed as a decimal)
• $n$ = Number of payments (loan term in years multiplied by 12)

To calculate the total interest paid over the life of the loan, you can subtract the principal loan amount from the total of all monthly payments.

Let's use an example to illustrate:

Suppose you have a 30-year fixed-rate mortgage with a principal loan amount ($P$) of $250,000 and an annual interest rate of 4.5%.

First, calculate the monthly interest rate ($r$):

Then, calculate the number of payments ($n$):

$n=30\times 12=360$

Now, plug the values into the formula to find the monthly payment ($M$):

So, the monthly payment is approximately $1266.71.

To find the total interest paid, use the formula:

So, the total interest paid over the life of the loan is approximately $207,615.60.

This calculation assumes that the interest rate remains constant throughout the entire loan term and that no additional payments are made towards the principal. Keep in mind that actual payments may vary slightly due to factors such as rounding and escrow payments for taxes and insurance.