Loan interest can sometimes feel like it’s magic. You get your credit card statement at the end of the month, and it has some interest amount on it. Or, you have a line of credit or a mortgage, and you see a breakdown of your payment. Some amount went to the principal, and a fraction of it went to interest. Seeing these numbers often makes people wonder how loan interest is calculated.
The good news is that even though the math might seem tricky, the loan interest amounts you see on your statements are relatively easy to calculate.
How Loan Interest Is Calculated: First, Some Terms
Before looking at how to do these calculations, let’s first discuss some terminology.
APR (or annual percentage rate) represents the full amount of interest that borrowers will have to pay over the life of the loan. This rate includes fees, compounding, and so on.
The interest rate is the amount the financial institution will charge, monthly or daily, to lend you the money.
Since the APR takes into account the interest rate, plus other factors, it is almost invariably more than the base interest rate. To illustrate with an example, let’s suppose that you’re looking at a five-year personal loan for $10,000. The interest rate is 5%. To process the loan, the bank charges you a $500 origination fee. The bank adds this amount to the loan. You will pay both the origination fee of $500 plus 5% interest on the money. Both of these count toward your APR, which makes it rise to 7.02%.
The principal is the amount of money that you have left to pay. Making extra payments towards your principal will result in the financial institution charging less interest for subsequent payments. Your monthly payments will not decrease, but more of them will go to paying off your loan, which enables you to pay it back faster.
A Breakdown of Loan Interest Calculations
How loan interest is calculated depends, partly, on the type of loan that you have. Credit card companies calculate interest much differently than regular loans (like mortgages or personal loans).
For credit card companies, the interest compounds daily. Let’s say, hypothetically, that your credit card’s APR is 25%. What a credit card company will do is divide that percentage by 365 to arrive at a daily rate. In this hypothetical example, your daily rate would be 0.0685%.
When you don’t pay off your balance in full by the due date, the credit card company multiplies your balance each day by that interest rate. They then add that amount to your balance. Each day, they repeat this process to determine how much interest you owe at the end of the month.
So, let’s say you started the month with a $1,000 total credit card balance. If your interest rate were 25%, then at the end of day 1, your credit card company would multiply $1,000 * 0.0685% = $0.68. That’s the amount of interest you’ll pay for that day.
Now, suppose you charge $100 to your credit card the next day. Your card’s new “balance” is $1,100.68. The credit card company will then multiply that by 0.0685% at the end of the day, which comes out to about $0.75. Adding that to the previous balance and you now have $1,101.43.
As you can see, the interest on credit cards adds up fast, and the daily compounding makes it add up even quicker! It’s usually very much in your best interest to pay off credit card debt as soon as possible for this very reason.
Amortizing Loans (Like Mortgages, Car, or Personal Loans)
Amortizing loans work much differently than credit cards. They do not have daily compounding. Instead, how loan interest is calculated for these loans is via the “simple” method.
To continue learning by example, let’s suppose you have $100,000 left on your mortgage at 4% interest (not APR, the simple interest rate). To calculate the amount of interest you will pay on these loans, all you need to do is take your interest rate, 4%, and divide by 12. That gives your monthly interest rate. In this case, it’s 0.33333%. Now, multiply your balance of $100,000 by 0.33333%, which is $333.33. That’s how much interest you’ll pay.
Of course, your payment isn’t strictly the interest. On an amortizing loan, you pay the accrued interest plus a portion of the principal. To arrive at your monthly payment, the bank uses a formula to determine the monthly payments, including the accumulated interest you’ll pay, over the number of payments you will make. That formula is a little complex (so get Excel or a calculator handy!).
It is: (rate per period)(present value) / (1 – (1 + rate per period) ^ -(number of periods)).
Let’s assume the mortgage amount was for $100,000 in our example above. The present value would be $100k. The rate per period would be 0.33333%. Assuming it was a 30-year mortgage, the number of payments would be 360.
Therefore, the monthly payment would be $477.42 = (0.3333%)($100k) / (1 – (1 + 0.33333%) ^ -360).
Your brief amortization schedule would look like:
- Your first month has a $477.42 payment, with $333.33 interest. Therefore, the company will deduct $144.09 from the principal of your loan. The new balance of the loan is $99,855.91.
- The second month has a $477.42 payment as well (this remains constant). Now, we multiply 0.0033333 * $99,855.91 to arrive at the amount of interest. That figure is $332.85. Now, we deduct that from $477.42 for a total of $144.57. When you subtract that from the balance of $99,855.91, you get $99,711.34.
- We use that new $99,711.34 balance for month three and perform the same calculations above.
This process keeps repeating for the duration of the loan until you pay it off. If you make a payment of extra principal, then it will lower the amount of interest you pay during the month since there’s less principal. It won’t lower your monthly payment, but more of it will go towards paying off the loan, which means you can close it out faster!
How Loan Interest Is Calculated: It’s Fairly Straightforward!
Ultimately, it’s relatively straightforward to calculate loan interest. First, you need to look at whether or not your interest is compounding daily or if it’s simple interest. Most credit cards have compounding interest. Lines of credit can also calculate interest in this manner. However, most other loan types (like mortgages) use simple interest calculations that calculate monthly interest and payments.
Then how loan interest is calculated is a matter of using a few formulas. Daily compounding interest is easy to calculate as you take the daily balance and multiply it by whatever the daily rate is. Calculating loan interest on mortgages and other amortizing loans involves dividing the interest rate by 12 and then multiplying the loan amount by that each month. Of course, how much your monthly payment is will determine how much of your principal you pay off for the next month.
One side effect of these loan calculations is that since credit cards use daily compounding interest, that makes them especially challenging to pay off. Therefore, if possible, avoid carrying a balance on credit cards!