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Financial Planning

How to calculate loan amortization?

Date:
October 13, 2021

"Amortization" sounds complex, but it describes the way you probably already think about loans. It's an awkward-sounding word that refers to making loan payments according to scheduled installments.

What are amortized loans?

Most personal loans, auto loans and home loans are amortizing loans. When you take out one of these loans, a flat monthly payment is usually specified. Throughout the life of the loan, your monthly payment will apply to both the principal and interest due on the loan, at shifting percentages, following a payment calendar usually stipulated by monthly payment periods. 

Beyond that, amortized loans can vary widely, with different payment amounts and different repayment schedules, depending on many variables, from the interest rate and the loan term to your lender's own requirements. 

For example, a 30-year mortgage and a 2-year personal loan can both be amortized, but the mortgage loan is likely to have more components, with different requirements for down payments, first payments and even special carve outs for extra payments.

With mortgages and auto loans, a high percentage of your initial payments often goes toward paying off interest on the loan. With each subsequent payment, more and more of your monthly payment goes toward the loan's principal. 

An amortization schedule reveals how much of each monthly payment goes to paying interest - showing you how much your loan is costing you over its full payment schedule. 

How to build a loan amortization schedule

Amortization calculators can be found across the internet. Most lenders offer financial calculators with online amortization charts. Spreadsheet software, like Microsoft Excel, often has amortization built in too. 

But here's how you can create your own amortization schedule, calculating the balance of interest and principle in each monthly payment. 

It takes a little math. But making your own loan amortization calculator is a good reminder of how much your loan costs you month by month.

Start by calculating your monthly interest payment. Multiply the loan's interest rate by the outstanding loan balance, then divide by twelve. This changes, of course, as you pay off more and more of the loan. 

Then calculate the amount of principal due. Take your flat monthly payment and subtract the month's interest payment. What's left over, the remaining balance, is the payment against your principal. 

The next month, subtract your most recent principal amount from the outstanding balance. The result is your new outstanding balance. Use that new balance to calculate your interest payment again. When you subtract your interest payment from your flat monthly payment, you'll have your new principal payment. 

Repeat the same math month after month until the end of the loan term, when your loan balance is zero.

How to calculate principal payments

Here's a formula for calculating your monthly principal payment on an amortized loan:

Principal payment = total monthly payment – (outstanding loan balance * (interest rate / 12 months))

However, if you're trying to estimate monthly payments based on given factors, such as the loan amount or the interest rate, you may need to calculate the monthly payment too. Here's a formula for calculating the total monthly payment:

Total monthly payment = loan amount  [ i (1+i) ^ n / ((1+i) ^ n) - 1) ]

where:

  • i = monthly interest rate. You'll need to divide your annual interest rate by 12. For example, if your annual interest rate is 3%, your monthly interest rate will be .0025 (.03 annual interest rate / 12 months).
  • n = number of payments over the loan’s lifetime. Multiply the number of years in your loan term by 12. For example, a 4-year car loan would have 48 payments (4 years * 12 months)

Let's look at an example

Let's look at a four-year, $40,000 personal loan at 3% interest. The monthly payment is going to be $664.03 ($30,000 ((.0025 (1.0025 ^ 48) / (1.0025 ^ 48) - 1))).

In the first month, $75.00 of the $664.03 monthly payment goes to interest ($30,000 outstanding loan balance * 3% interest rate / 12 months) while the remaining $589.03 goes toward principal ($664.03 total monthly payment - $75.00 interest payment).

Each month, the total payment stays the same, while the portion of the payment going to principal increases and the portion going to interest decreases. In the final month, only $1.66 is paid in interest because the outstanding loan balance at that point is so small.

What's the difference between amortization and depreciation?

Amortization and depreciation are almost the same, except in specific accounting concerns. Both look at the cost of holding an asset, including the cost of paying off a loan over time. However, amortization can include intangible assets, like intellectual property, patents and trademarks, while depreciation considers only tangible assets, like equipment and buildings - things that can show physical wear and tear.

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MoneyScience™ Team
Bright Money

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