Understanding amortized loans and how to calculate mortgage payments
Quick insights
- “Loan amortization” refers to the repayment schedule for a loan, including a breakdown of interest and principal payments.
- Amortized loans include a loan schedule, which is provided before signing, showing exactly how much money will go toward the principal and interest each month.
- Payments are fixed, but the unpaid balance gradually decreases, with less of each monthly payment going toward interest, and more going toward principal.
Whether you’re buying a home or already have a mortgage, knowing how amortized loans work can be helpful. In this article, we’ll cover key concepts and show an example of an amortized loan schedule before diving into more advanced questions. Finally, we’ll provide a few suggestions to help borrowers manage and potentially optimize their amortized loans.
What is loan amortization?
Before finalizing your mortgage, you’ll be presented with the proposed amortization schedule. By definition, “amortization” refers to a schedule for the loan which shows the total payment for each month, including how much will go toward the interest vs. paying down the principal balance of the loan. Check your understanding on these key concepts:
- Loan principal: This is the amount of money borrowed with a mortgage that goes directly toward the purchase of the home.
- Interest rate and amount: With a fixed-rate loan, you’ll be approved for one interest rate that is consistent throughout the loan schedule. Each month, you’ll pay this rate in addition to your principal balance.
- Term: This is the length of the loan. Conventional mortgage terms are typically 15 or 30 years long and repaid monthly. As a baseline, a 30-year mortgage includes 360 monthly payments.
Loans with amortization schedules start with a higher percentage of each payment going toward the loan’s interest; as the loan amount decreases, so does the amount paid toward interest. The result is a fully repaid mortgage.
How monthly payments are calculated
Most conventional mortgages follow amortized repayment schedules. The loan is repaid over all the years in the loan term with same-size payments. An amortization schedule’s fixed monthly payment is calculated using a specific formula:
M = P x r x (1 + r) n / (1 + r) n -1
In this formula, M represents the monthly payment, P is the principal, r is the monthly interest rate (annual rate divided by 12) and n is the total number of payments.
Let’s look at an example where the total loan is $200,000, with a 5% interest rate.
- P = 200,000 (the principal)
- r = 0.05 / 12 ≈ 0.004167 (the monthly interest rate)
- n = 360 (the total number of payments for a 30-year mortgage)
When calculated, this provides a fixed monthly payment of M ≈ $1,073.64.
Calculating the first month’s interest and principal
Working with the same example, let’s break out the cost paid toward the interest and principal for the first month of an amortization schedule. This process includes:
- Principal x monthly interest rate = Interest amount
- Monthly payment – interest = Principal payment
- Old balance – principal payment = New loan balance
Plugging in the same numbers as before, the first month’s interest and principal costs will be approximately as follows:
- $200,000 (principal) x 0.004167 (one month’s interest) = $833.40 interest paid.
- $1,073.64 (fixed monthly payment) – $833.40 (interest paid) = $240.24 principal payment.
- $200,000 (principal) – $240.31 (principal payment) = $199,759.69 remaining on the loan.
You’ll notice that the interest payment does not diminish the principal balance. The next month’s calculations will then start with the remaining principal of $199,759.69. The first three months will look like this:
Month 1:
- Payment: $1,073.64
- Interest: $833.33
- Principal: $240.31
- Remaining Balance: $199,759.69
Month 2:
- Payment: $1,073.64
- Interest: $832.33
- Principal: $241.31
- Remaining Balance: $199,518.38
Month 3:
- Payment: $1,073.64
- Interest: $831.33
- Principal: $242.31
- Remaining Balance: $199,276.07
In these first few months, the shift between the size of interest and principal payments may seem subtle. However, as months turn to years, the remaining balance will gradually reduce, with interest payments shrinking as a result.
The final months of an amortized loan schedule
By the end of the amortization schedule, the proportions of the payment will have changed completely. To illustrate this change, look at the final three months of the schedule, assuming the borrower stays on track with their payments:
Month 358:
- Payment: $1,073.64
- Interest: $4.45
- Principal: $1,069.19
- Remaining Balance: $2,145.92
Month 359:
- Payment: $1,073.64
- Interest: $3.57
- Principal: $1,070.07
- Remaining Balance: $1,075.85
Month 360:
- Payment: $1,073.64
- Interest: $0.45
- Principal: $1,073.19
- Remaining Balance: $0.00
Strategies to manage mortgage amortization
In general, fully amortized mortgages with a fixed interest rate are considered the most predictable. Their complete payment schedules can be seen at-a-glance before signing. For many borrowers, this makes them the easiest to manage. However, a potential downside could be that the rates are not favorable when you happen to apply for the loan and can’t be changed until you refinance.
Although amortized loans seem fully planned out, there are still ways a borrower can manage repayment over the loan term.
- Making extra payments: Making extra payments or larger monthly payments toward the principal specifically can help shorten the loan term and reduce interest. For example, an extra $100 per month designated toward the principal of the original $200,000 loan example could reduce the total repayment period by up to 5 years.
- Refinancing to a better rate or shorter term: Your original mortgage’s interest rate is influenced by several factors, including market conditions and your credit history. These things can change with time. Refinancing at some point in your loan term may result in lower rates or a shorter term. Refinancing a mortgage loan will result in a new repayment schedule, likely amortized depending on the loan type and terms.
FAQs about amortization loans
Does the amortization schedule change with extra payments?
Yes, an additional payment can change the loan term and lower the total interest paid. However, the lender may charge a penalty for early repayment—review your loan agreement and contact your lender for more information.
Can I request an amortization schedule?
Yes, if you request one, your lender should be able to provide an amortization schedule for your mortgage loan.
In summary
Understanding how amortization works can help you plan ahead and make decisions when it comes to repaying your own mortgage. An amortization schedule will show how interest and principal is applied with each monthly payment until the loan is paid in full. If you’re thinking about buying a home soon and want to discuss your mortgage options, consider reaching out to a Chase Home Lending Advisor .
