Loans and interest are tricky, and so is calculating total interest on them. You have probably heard terms like “simple interest,” “compound interest,” and “APR,” but may be unsure what they mean.
To understand and calculate the total interest, you need to know the type of interest and how it is calculated on a periodic basis. The good news is there are only three types, and the differences are easy to understand with examples.
We’ll cover these basic types and look at total interest formulas and calculators below. Note that total interest is distinctly different than total debt. Note also that this article does not address other interest that appears on company’s financial statements.
Definition of Total Interest
Total interest is the sum of all interest paid over the life of a loan or interest-bearing account, including compounded amounts on unpaid accumulated interest. It can be derived using the formula [Total Loan Amount] = [Principle] + [Interest Paid] + [Interest on Unpaid Interest].
This may seem complicated, but we’ll clear it up with examples in Excel for each type below.
Total Interest Formula
The formula for total interest is [Total Interest] = [Interest Paid] + [Interest on Unpaid Interest] = [Total Loan Amount] – [Principle].
Total Interest Excel Calculators
You can get the Excel used in the article below. It has every loan schedule you’ll ever need (variable rate, additional payments, compounding unpaid interest, and revolvers) and a built-in total interest calculator so you can easily compare options.
That said, using the calculators requires knowledge of the mechanics of each interest type. I encourage you to read through the article to ensure you make best use of the calculators.
Download Excel Calculator Here!
Types of Interest
- Simple Interest
- Compound Interest
- Interest on Revolver
Simple Interest (Base)
Simple interest is what lenders use for mortgages. This type of interest is calculated on the outstanding balance of loan principle in a given period. Usually there are a fixed number of periods in which this interest is calculated.
Together, the interest rate, the principle amount, and the number of periods are combined to establish a fixed payment in each period. This fixed payment remains stable when you make early payments, but the number of payment periods will reduce. Thereby, so will your total interest paid.
However, if you have a variable rate (see section at end of article), the value of the fixed payment will change.
Here’s a sample model for a 12-month loan for $150,000 at 4%. In this base scenario, no additional payments are made and the interest rate remains stable.
Total Interest on Simple Interest Loan
To calculate total interest on a simple interest loan, simply add the sum of the interest line, which amounts to $3,270 in the above example.
Note that total interest is different than interest yield.
Simple Interest (Additional Payments)
Now here’s what it looks like when we add an additional payment twice as large as the normal payment in month 6 (i.e paying three times in that period).
Now we can see that the principle of the loan is paid off in month 10 rather than month twelve, even though the payment amounts remain stable.
On the italicized line labeled “rate check” you can see that the relative monthly interest becomes higher. This is because the interest payment remains stable but the principle amount has decreased. However, since you pay the loan off earlier, you pay two periods less of interest.
Total Interest on Simple Interest Loan with Additional Payments
To calculate total interest on a simple interest loan with additional payments, take the sum of interest paid for the full length of the loan minus the sum of interest in periods removed due to early payment. In this example, total interest is $3,016, or $254 less than the simple loan.
Simple Interest (Variable Rate)
Now let’s look at a variable interest rate. Let’s take our base case and modify the interest rate from 4% to 6% in month 7.
With a change in the variable rate, the monthly payments increase as well. You can think of the impact of a variable rate as “what the interest would have looked like in this period if the whole loan duration used this interest rate.”
Because the original principle and number of periods is the same for both interest rates, the amount is paid off in the same number of periods, but the rate in a given period changes.
Total Interest on Simple Interest Loan with Variable Rate
To calculate total interest on a simple interest loan with a variable rate, simply add up the interest payments for each period of the loan with the knowledge that these will vary in relative size depending on the rate used. In this example, total interest is $3,657, or $387 more than the base case.
Compound Interest
Simply put, compound interest is interest paid on interest.
Compound interest is most common in special savings accounts, where a principle amount accrues interest at a fixed rate during a period, then that accrued interest is “added” to the principle amount in the subsequent period and produces more interest — i.e “interest on interest.”
For example, imagine you have a deposit for $100 in a 1% yearly interest account. In the first year, you earn $1 in interest. That value is now added to your principle amount, totaling to $101. In the second period, you earn interest on $101, or $1.01, so your new balance is $102.01, which then earns more interest, and so on.
In a loan, compound interest can occur when the debtor fails to pay the interest portion of a periodic payment (although this usually only happens when an entire payment is missed, since a partial payment can usually be first applied to the interest amount). This is called unpaid interest.
In this scenario, the value of unpaid interest can be tracked in a separate schedule. It grows in each period on a compounding basis until paid in full.
NOTE: In some rare cases when the interest becomes too large for the debtor to settle in a reasonable time, a new loan schedule can be created, where the accumulated unpaid interest becomes the principle amount of the new loan. Here’s what the separate schedule scenario might look like:
As you can see, in months 7, 8, and 9, interest was not paid. The mechanics of this schedule are more straightforward than they seem. The unpaid interest and accumulated unpaid interest are summed together, then any direct payments on the balance are subtracted. In each period the outstanding balance is multiplied by [1+rate], and is compounded as such.
It’s important to realize that these amounts are only paid back once the base payment in each period is covered. You cannot choose — unless specifically arranged between lender and debtor — to pay accumulated interest before the current period’s principal and interest payment.
Total Interest on Compound Interest
Total interest on in a compound interest scenario is equal to the sum of interest in the life of the loan plus interest on unpaid accumulated interest before settlement. In this example total interest is $3,281, or $11 more than the base case.
Interest on Revolver
Revolver loans allow continual draw down of principle amounts (called the balance) across periods and calculate interest on a rolling basis. Unpaid interest is so called “capitalized,” meaning it is added to the principle amount just like unpaid interest in compounding loans.
There are two primary applications for revolver loans: credit cards (APR), and revolving credit facilities to companies. Credit card revolvers are compounded on a daily basis but include a monthly grace period, and revolvers to companies are compounded on a monthly basis.
Let’s look at both.
Credit Card Revolvers (APR)
Credit card revolvers allow holders to draw down debt on a rolling basis, often with the swipe of a card. The interest rate is called annual percent rate (APR) and on average is 15%. The APR is divided by 365 to get the daily rate — the daily rate is what’s important to consumers, and would be 0.041% on an ARR of 15% for example.
Each day the cardholder uses credit, the amount is added to the balance. Interest is charged on the balance at the daily rate and at the end of the day it becomes the new balance. If it’s not paid off, the balance incurs interest each day until paid. A 0.041% rate may not seem high, but when compounded over a month, it is certainly non-trivial for large balances.
That said, virtually all credit card issuers have a grace period in which no interest is charged on a balance as long as it is paid by a given day of the month, usually the 15th or the last day.
For example, imagine a cardholder has a credit line of $1000/month with an APR of 15%. S/he uses $300 on January 1st. On January 2nd, her balance is $301.23 (300 + 300 * 0.0041). Let’s imagine two scenarios: one where she pays by the last day of the month (grace period) and one where she does not make the payment.
As you can see, when the grace period is not met, the cardholder accumulates $3.85 in interest. However, when the grace period is met, s/he pays no interest.
Total Interest on Credit Card Revolver
Total interest on a credit card revolver is the sum of accumulated daily interest during the month when the cardholder does not meet the grace period payment. In the example above, total interest is $3.85.
Revolving Credit Facility to Companies
The mechanism for revolvers to companies is very similar to credit cards. The key difference is that interest does not usually accumulate on a daily basis, but a monthly one.
A company may establish a revolving credit facility when it has a delay between cash in from operations and obligations to pay suppliers.
For example, a company that needs to make payments of $100,000 in the beginning of the month but has steady inflows of $200,000 throughout the month may use revolving credit to ease its cash outflow. And since it will pay the credit balance by the end of the month, it incurs no interest. This is just one example.
Total Interest on Revolvers to Companies
Total interest on revolvers to companies is calculated as the sum of interest incurred over the life of the revolver, where accumulated interest is compounded on a monthly basis.
Interest Terms to Know
In addition to the 3 types of interest explored above, it’s important to be familiar with some additional terms to understand how they can impact total interest.
- Interest capitalization. The placement of accumulated interest into the interest-bearing principle amount. This is the process by which interest compounds.
- Fixed rate. A fixed rate is an interest percentage that does not change over the life of the loan. Most mortgages and other commercial loans typically have fixed rates.
- Variable rate. A variable rate is one that changes over the life of the loan, typically as a function of the prime interest rate (see next point).
- Prime Interest Rate. The interest rate large banks charge their most creditworthy customers, typically large corporations, i.e the lowest rate in the market. This is the metric on which variable interest rates are based. Movement in the prime rate influences the variable rate on other loans.
Conclusion
Total interest depends on the type of loan and its mechanics, namely whether there are early payments on principle, variable interest rates, or missed interest payments. In general, total interest is equal to the sum of all interest paid over the life of a loan or interest-bearing account. Moreover, total interest on revolvers can be compounded daily or monthly, but grace periods allow debtors to avoid paying any interest at all.
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