# How to calculate interest rate

Most Americans have a relationship with interest: accrued on savings, owed on student loans or compounded in a 401k. But how is interest calculated? You likely know your rate (or maybe your APR. there's a difference), but how does that number turn into money gained or owed?

Math doesn't need to be your strong suit to follow along and learn what is perhaps the defining element of a loan: the interest rate formula.

## What is interest and how does it work?

When you stop and think about it, interest as a concept has an exceedingly reasonable foundational logic. Banks, credit card companies, mortgage providers and other lenders are engaged in a money-lending business—a for-profit business. And that business involves a degree of risk every time money—known in lending circles as the “principal”— is lent to a borrower.

## How interest works

To account for risk—and to ensure the business generates a profit—lenders tack on an interest payment in addition to the principal amount that you are expected to pay back in full over a designated period of time. This interest is almost always expressed in the form of a percentage rate such as 3%. As you pay back the principal over a select amount of time, you will also be paying a smaller but regular interest payment based on your interest rate.

It’s worth noting that your interest rate is not the same as your annual percentage rate (APR). APR is a broad measure of all expenses you owe expressed as percentage. These expenses include (most) closing costs, mortgage insurance, discount points (if applicable) and loan origination fees.

Grasping the broad strokes is the easy part. The more challenging aspect is to understand why interest rates fluctuate from day to day and from lender to lender. On a broad level, current interest rates are a reflection of the Federal Reserve’s monetary policy as well as the yield on the 10-year Treasury notes. This mystery is further deepened when you understand that there aren’t just macroeconomic factors influencing your interest rate, but such things as your own credit history, credit score, recurring debt and available assets and income. Including these factors into the interest calculation mix is an important way lenders account for risk and protect themselves from financially unfit borrowers who may be more likely to miss payments or default on their loans altogether.

Alternatively, if your creditworthiness is deemed exceptional, your lender will likely assign you the lowest rate available.

## Calculating with an interest rate formula

Lenders entertain different methods to calculate risk depending on the type of loan. Let’s look at a couple of the most popular interest calculation methods.

### Simple interest

Simple interest sounds, well, simple enough, and it is for the most part, but it comes with a wrinkle or two that add some complexity. The important thing to remember is that simple interest is calculated only on the original loan balance. The interest does not grow over time based on previous interest payments. It does not compound.

For prospective homebuyers, it’s worth noting that simple interest is a calculation method often (but not always) used to determine interest for home mortgages, as well as personal loans, auto loans and student loans. However, there are other ways of determining interest we’ll talk about in a moment.

When determining simple interest, you’ll need to gather some very basic (but relevant) information. Once you have that, determining the interest due is pretty easy.

There are two simple interest rate formulas.

#### How to calculate interest: total simple interest formula

The simple interest formula for calculating total interest paid on the loan is:

Principal x interest rate x number of years = total interest due on loan

**Example 1***

If you take out a $200,000 mortgage at 4% interest over a 30-year term, the calculation looks something like this:

$200,000 x 0.04 = $8,000

That’s the total interest you will pay over the life of your loan*

#### Daily simple interest formula calculation

Opening balance x (interest rate ÷ 365) x number of days between payments =

interest due for the month

**Example 2***

$200,000 x (.04 ÷ 365) x 30 = $21.9

Multiply that number by 30 and you get $657.5. That’s the monthly figure.*

### Amortization and interest

You will almost certainly be presented with an amortization schedule once you are set to close on your mortgage. This will be evident both in the Loan Estimate and the Closing Disclosure.

## How does an amortization schedule work?

If you have a fixed rate loan, the amortization schedule will provide you with a table that lists all the fixed payments over the life of your loan—including a breakdown of both interest and principal. Note: The payments are fixed but the ratio between the amount of principal paid each month and amount of interest paid will constantly shift.

It’s typical for the first half of the loan to emphasize interest payments over principal. After a certain point, which will be evident in your amortization schedule, you will begin paying more principal and less interest until finally the loan is paid in full.

### Amortization and compound interest

Compound interest is when the unpaid or accumulated interest at the end of the first period (or the first month) is added to the principal for the second period (the following month), allowing the interest to compound. This is often referred to as “interest on interest.” As you can imagine, this results in higher interest payments.

The good news is that compound interest is **not** a common method for determining interest for home mortgages here in the U.S.** Your mortgage interest is actually calculated on a backward-looking monthly basis, which is to say it’s paid in arrears.

For example,* the September payment on your mortgage is for August interest and September principal. That's why when you close your loan you don't make your first payment the next month; you make it the following month and just pay interim interest for the month you close in. A September 10th closing date, for example, would mean a November 1st first payment that includes October interest. At closing, you’ll pay the interim interest for September on the amount you borrowed (22 days of interest).*

It can all sound a little confusing, but if you look at your loan estimate and particularly your closing disclosure, there should be a table that accounts for future projected payments over 360 months (for a 30-year loan). That’s the beauty of an amortization schedule: It creates visibility into the entire repayment of the loan + interest. There are no surprises.

#### Amortization formula: total monthly payment and interest payment

The formula for determining your monthly mortgage payment is as follows:

**M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]**

P = principal loan amount

i = monthly interest rate

n = number of months required to repay the loan

**Example***

Let’s go back to our previous loan numbers. Let’s say you have obtained a 4% interest rate on a $200,000 loan (the home is priced at $255,00 and you put 20% down leaving you with a principal of $200,000).

A simple mortgage calculator uses the following information to calculate the total monthly payment:

- Principal: $200,000
- Interest rate: 4%
- Mortgage term (years): 30
- Mortgage term months: 360

Using the formula above or simply inputting the numbers into a convenient mortgage calculator, you find that you will owe a consistent payment of $954.83 (not including homeowners insurance, property taxes and other fees).

From here, a simple formula for interest would be:

**(Interest rate ÷ # of annual payments) x remaining balance = monthly interest paid**

Using the same number above, we can determine that interest will be $667.67 for the first month. Calculating the principal is now a cinch:

$954.83 - $667.67 = $288.16

**The balance on your loan is now $199.711.84**.

In month two, using the same interest rate, same mortgage terms but your new balance, you’ll notice that your principal and interest payments change but that the overall monthly payment remains the same.

**Month two:***

- Monthly payment: $954.83
- Principal payment: $289.12
- Interest payment: $665.71
**New balance: $199.422.71**

While your monthly payment remains fixed, your principal and interest continue to adjust every month as is evident in these amortization examples. This is commonly referred to as paying interest in arrears.

## Other factors that affect your interest

We mentioned earlier that there are larger economic forces at work as well as more individualized elements that affect interest paid on a loan. Let’s take a look at some of these factors.

### Amount of money borrowed

When it comes to interest, principal matters. While the borrower’s objective is to always hunt around for the optimal interest rate, no matter how low your rate is, you’ll still be on the hook for monthly interest payments. That said, total interest paid is not exclusively determined by your mortgage rate. The amount of money borrowed—the size of the principal—also has a determinative impact on the total amount of interest paid.

For example, If you get a home loan for $100,000 at 3% interest, your total interest payments will be markedly less than a 3% rate for a $200,000 loan.* It’s not just the principal amount that will be greater. But the greater the principal, the more interest paid to your lender over the life of your loan.

### The interest rate itself

The particular interest rate assigned to you is the result of larger market data working in concert with your financial profile. And when we say “financial profile” we really mean credit score. While your debt-to-income ratio and loan-to-value ratio are also key factors, perhaps no single influence is more important to optimizing interest rate than an excellent credit score. A very good or great credit score can help make you eligible for superior interest rates.

A difference of even 1% can have a significant impact on the amount of interest you ultimately pay on your mortgage. Consulting an amortization schedule, a $200,000 mortgage at 4% interest over a 30-year term would generate $143,000 of total interest.*

That same $200,000 with an interest rate of 3% would yield significant savings over a 30-year term: $103,554 (versus $143,000). The total monthly payment is also less: $843.21 vs. $954.83.*

The takeaway? Credit scores matter immensely when it comes to obtaining the best interest rates. And with lower rates, come lower monthly payments and lower overall interest paid.

Calculating interest is one thing. Building up good credit over a number of years so your credit score is in the top bracket is something else entirely. Always check your credit score in the months leading up to your big decision to ensure it’s in a range that will help you lock in an optimal rate.

### Loan term

If you want to minimize total interest paid over the life of your loan, you’ll want to choose a shorter loan term. The classic distinction is between a 30-year mortgage and a 15-year mortgage. While a 30-year mortgage has a clear advantage when it comes to lower monthly payments, the 15-year loan will actually incur less interest overall—significantly so.

- $200,000 30-year mortgage with 3% interest = $103,554*
- $200,000 15-year mortgage with 3% interest = $48,608*

Massive difference, right? Presented solely with this information, it might seem like a no-brainer to go with the 15-year term. However, overall monthly payments are visibly higher:

- Total monthly payments 15-year term = $1,381.16*
- Total monthly payments 30-year term = $843.21*

Many borrowers are not entirely comfortable dealing with a recurring monthly expense of this magnitude. Ultimately, it’s an issue of affordability. If you qualify for both loans, you might want to think about the pros and cons of lower monthly payments vs. higher amount of overall interest paid.

## In conclusion

Understanding the various ways to calculate interest and how interest affects your monthly and cumulative mortgage payments is an important part of the homebuying process. While a quoted interest rate is one of the most visible driving factors behind home purchases and refinances, borrowers don’t always put a lot of thought into the concept and calculation methods of interest.

By familiarizing yourself with the process, you can gain increased knowledge into how your monthly payments are structured, and what questions you need to ask your lender as you approach a home purchase or seek a refi.

*All sample loan scenarios are not advertised loan options and are provided only for illustration purposes and are not intended to provide mortgage or other financial advice specific to the circumstances of any individual and should not be relied upon in that regard. Guaranteed Rate, Inc. cannot predict where rates will be in the future

**The only mortgage loans that use compound interest are negative amortization loans such as the option ARM. Guaranteed Rate does not offer negative amortization loans.

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