How to Calculate Principal and Interest
The loan amount that you borrow is called the principal, and the interest represents the cost of borrowing charged by the lender. To calculate the principal and interest, multiply the principal amount by the interest rate and multiply the result by the number of years in the loan. Calculating the principal and interest tells you how much a simple interest loan will cost you.
However, the principal and interest calculation gets more involved if the loan uses another interest calculation, such as an amortized loan (a mortgage) or compound interest (a credit card). With simple interest, your interest payments remain fixed, while amortized loans charge you more interest earlier in the loan. Learn the types of interest that lenders can charge you and how to calculate a loan’s principal and interest using an example of a mortgage.
Key Takeaways
- To calculate the principal and interest on a simple interest loan, multiply the principal by the interest rate and multiply the result by the loan term.
- Divide the principal by the months in the loan term to get your monthly principal payment on a simple interest loan.
- A loan calculator is helpful when calculating amortized loans to determine the amortized interest payments, which gradually decrease over the course of the loan.
- With fixed-rate loans, your monthly payment will be consistent for simple or amortized interest-based loans.
Principal and Interest
When you make a loan payment, part of it goes toward interest payments, and part goes to paying down your principal. Understanding how banks and credit unions calculate these components can help you understand how you will pay your loan down.
Principal
The principal is the original loan amount, not including any interest. For example, with mortgages, suppose you purchase a $350,000 home and put down $50,000 in cash. That means you’re borrowing $300,000 of principal from the mortgage lender, which you’ll need to pay back over the length of the loan.
Interest
The interest is the amount the bank charges for lending you money. Generally, shorter-term, fixed-rate loans like personal loans use a simple interest calculation. Longer-term loans like mortgages and some auto loans are amortized.
Example of Mortgage Interest Calculation
Let’s say the loan in the example above is a 30-year mortgage with a 4% annual interest rate that is amortized. Because you’re making monthly payments, the 4% interest rate gets divided by 12 and multiplied by the outstanding principal on your loan. In this example, your first monthly payment would include $1,000 of interest ($300,000 x 0.04 annual interest rate ÷ 12 months).
If you input your purchase price, down payment, interest rate, and the length of the loan into the Investopedia Mortgage Calculator, you will see that your monthly payments to the lender would equal $1,432.25. As noted earlier, $1,000 of your first payment strictly covers the interest cost, meaning the remaining $432.25 is paying down your outstanding loan balance or principal.
The example above doesn’t include other costs, such as mortgage insurance and property taxes held in escrow.
How Amortization Works
If you have a fixed-rate loan, your monthly mortgage payment remains the same. In theory, the interest rate is being multiplied by a shrinking principal balance. The reason the amount you pay does not decline is that lenders use amortization when calculating your payment, which is a way of keeping your monthly bill consistent.
Note
With amortization, your monthly payment is comprised mostly of interest in the early years, with a smaller portion of the payment going toward reducing the principal.
Example of Amortization
Sticking with our earlier example and assuming you don’t refinance, your loan payment will be the same 15 years later. But your principal balance will be reduced. In 15 years, you would have a remaining balance of approximately $193,000 of the principal on your loan.
Multiplying $193,000 by the interest rate (0.04 ÷ 12 months), the interest portion of the payment is now only $645.43. However, you’re paying off a bigger portion of the principal, meaning $786.82 of the $1,432.25 monthly payment is going toward the principal.
The table below shows the monthly payments at various points in the 30-year mortgage. You’ll notice that the interest portion of the monthly payment declines while the principal portion increases over the life of the loan. You can use an amortization calculator to help you determine your own loan’s interest and principal amounts.
| Mortgage Loan Amortization With Principal and Interest Breakdown | |||
|---|---|---|---|
| Year | Principal | Interest | Monthly Payment |
| Year One | $432.25 | $1,000 | $1,432.25 |
| 15 Years | $786.82 | $645.43 | $1,432.25 |
| 20 Years | $960.70 | $471.54 | $1,432.25 |
| 30 Years | $1,427.49 | $4.76 | $1,432.25 |
During the last year of your mortgage, you’re paying off mostly principal and very little interest. By leveling out your payments like this, mortgage lenders are making your payments more manageable. If you paid the same amount in principal over the course of the loan, you’d have to make much higher monthly payments right after taking out the loan, and those amounts would plummet at the tail end of the repayment.
If you’re wondering how much you’ll pay toward principal versus interest over time, the Investopedia Mortgage Calculator also shows the breakdown of your payments over the length of your loan.
Adjustable-Rate Mortgages
If you take out a fixed-rate mortgage and only pay the amount due, your total monthly payment will stay the same over the course of your loan. The portion of your payment attributed to interest will gradually go down as more of your payment gets allocated to the principal. But the total amount you owe won’t change.
However, it doesn’t work that way for borrowers who take out an adjustable-rate mortgage (ARM). They pay a given interest rate during the initial period of the loan. However, after a certain length of time—one year or five years, depending on the loan—the mortgage “resets” to a new interest rate. Often, the initial rate is set below the market rate at the time you borrow and increases following the reset.
Your monthly payment can change on an adjustable-rate mortgage, because your outstanding principal is being multiplied by a different interest rate.
Interest Rate vs. APR
When receiving a loan offer, you may come across a term called the annual percentage rate (APR). The APR and the actual interest rate that the lender is charging you are two separate things, so it’s important to understand the distinction.
Unlike the interest rate, the APR factors in the total annual cost of taking out the loan, including fees such as mortgage insurance, discount points, loan origination fees, and some closing costs. It averages the total cost of borrowing over the duration of the loan.
It’s important to realize that your monthly payment is based on your interest rate, not the annual percentage rate. However, lenders are required by law to disclose the APR on the loan estimate they provide after you submit an application, so that you can have a more accurate picture of how much you’re actually paying to borrow that money.
Some lenders may charge you a lower interest rate but charge higher upfront fees, so including the APR helps provide a more holistic comparison of different loan offers. Because the APR includes associated fees, it’s higher than the actual interest rate.
The formula to calculate the principal and interest on a simple interest loan is SI = P * R * T whereby:
- P = principal or borrowed amount
- R = interest rate
- T = time or the number of years in the loan
Frequently Asked Questions (FAQs)
How Is My Interest Payment Calculated?
Lenders multiply your outstanding balance by your annual interest rate but divide by 12 because you’re making monthly payments. So if you owe $300,000 on your mortgage and your rate is 4%, you’ll initially owe $1,000 in interest per month ($300,000 x 0.04 ÷ 12). The rest of your mortgage payment is applied to your principal.
What Is Amortization?
Amortizing a mortgage allows borrowers to make fixed payments on their loan, even though their outstanding balance keeps getting lower. Early on, most of your monthly payment goes toward interest, with only a small percentage reducing the principal. Over time, it switches, whereby a greater portion of your monthly payment reduces your outstanding balance, and a smaller percentage goes to interest.
What’s the Difference Between Interest Rate and APR?
The interest rate is the amount the lender actually charges you as a percent of your loan amount. By contrast, the annual percentage rate (APR) is a way of expressing the total cost of borrowing. Therefore, APR incorporates expenses, such as loan origination fees and mortgage insurance. Some loans offer a relatively low interest rate but have a higher APR because of other fees.
The Bottom Line
You likely know the monthly payment for your mortgage, auto loan, or personal loan. However, calculating how that money is divided between principal and interest can help you understand how much your loan will cost you and how your loan will be paid down. You can make those calculations yourself or turn to an online loan calculator.