Even for experienced finance professionals, interest is a tough topic. Between fixed, variable, simple, accumulated, accrued, and others, I find myself needing a review from time to time. Specifically, **accrued interest** and **compound interest** are easy to confuse because they both “grow” over time, just not in the same way.

In this article we’ll define the terms, look at formulas, show examples, address the time element behind these financial mechanisms (namely days vs months), and finally look at Excel calculators you can download.

## Accrued Interest vs Compound Interest: What’s the Difference?

First thing’s first — we need a succinct description of the difference to set the pace for the rest of the article. For both accrued and compound interest, we’re dealing with 3 parts of a mechanism: (1) a base amount of value (the “principle”), (2) a percent increase on the principle (the “interest”) and (3) a catalyzing moment (the “term”).

**The difference between accrued interest and compound interest is that accrued interest is calculated (1) at each term (2) on the beginning principle amount only, such that interest grows as a running total over time, whereas compound interest is calculated (1) at each term (2) on the beginning balance (3) plus any unpaid interest, such that interest grows “on itself” — i.e it is compounded.**

For example, imagine a beginning balance of $1,000 with three terms and an interest rate of 10%. Under accumulated interest, the final balance would be **$1,300** (1,000*(1+10%)+1,000*(1+10%)+1,000*(1+10%)), whereas under compound interest the final balance would be **$1,331** ($1,000*(1+10%)*(1+10%)*(1+10%)).

## Definitions: Accrued Interest vs Compound Interest

### Accrued Interest

By definition, accrued interest is the sum of all unpaid interest on a financial note, whether that interest is calculated on a compound basis or a simple accrued basis. By this definition, accrued interest is the same as **accumulated interest**.

However, in day-to-day talk you will hear it used as *a way to differentiate* from other interest *calculation* methods, namely **compound interest**.

Moreover, accrued interest is also a technical term in accounting that refers to any amount of interest that has been incurred (meaning the catalyst term has passed) and the amount **is due** to be paid in the period, but the cash transfer has not yet occurred.

Accounting accrued interest is different than normal accrued interest because in the former an interest payment has become due, whereas in the latter a payment is not due, but it *is* accumulated. Moreover, normal accrued interest is only “due” at the expiry date of the financial note.

I know it sounds like there’s crossover between the words and their meanings. That’s because in day-to-day talk people use “accumulated” and “accrued” in a number of different ways. It’s up to you to discern which is correct *based on contex*t.

For the most part, however, we can summarize with the following statements:

- Accrued interest is interest calculated on an original principle amount only
- Accrued interest can refer to all unpaid interest on a note, whether calculated on the principle only, or compounded
- Accumulated interest can be used as a synonym for accrued interest in the two cases above
- Accrued interest in accounting refers to interest payments that are due to be paid in a period but for which no money has been transferred

### Compound Interest

By definition, compound interest is interest calculated on both the principle amount of a financial note and any accumulated interest from previous periods.

Compound interest is arguably the most powerful force in finance. Its capacity to grow over time can make investors rich. Albert Einstein is recognized for saying, “Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.”

We’ll look at comparative examples in the sections below to flush out the idea of compounded interest fully.

Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.

Albert Einstein

Note, whether the mechanism is accrued or compounded interest, we can calculate the total interest of a loan. This amount is then used to calculate the interest yield of a loan for the lender.

On a company’s financial statements, interest is usually shown as a P&L line item, but can in some cases be listed under other interest.

## Formulas: Accrued Interest vs Compound Interest

### Accrued interest

As a formula, **accrued interest = rate * principle amount * number of periods**.

Or more simply,** accrued interest = r * principle amount * n**.

### Compound interest

**Compound interest = principle amount * (1+r)^nt**, where r is the rate, n is the number of times interest accrued in a period periods, and t is the number of periods.

Simplified, we can write simply **compound interest = principle amount * (1+r)^n**, where n is *both the number of period and the number of times interest compounds*, i.e n=t.

## Daily Interest vs Monthly Interest

Due to the exponential growth of compound interest, it’s often calculated on a **monthly** or **yearly** basis. Accrued interest, on the other hand, is often calculated on a daily basis.

### Monthly Basis

Imagine you have a small loan for $1,000 that’s payable in 6 months with a **monthly** compounding interest rate of 3%. Additionally, imagine you have a the same loan of $1,000 that’s payable in 6 months with a **monthly** accrued interest rate of 3%. They would look like this as schedules:

Download Excel Template Here

As you can see, the compounding scenario produced a total obligation of $1,194 vs $1,180 in the case of a simple accrued loan, or **11%** more due.

Ok, so the difference isn’t shocking. But what happens if we make the interest calculation more frequent, I.e on a **daily basis** for six months?

### Daily Basis

Look what happens when we adjust the interest computations to a daily view:

Download Excel Template Here

As you can see, the difference is staunch. Accrued interest on a daily basis results in $6,400 due at the end of the schedule, which is $5,220, or 340%, higher than the monthly computation.

Moreover, compound interest is $45,852, or 3740% higher than the monthly computation at the end of the schedule.

Perhaps most relevant is that compound interest on the daily view is $40,646, or 635%, higher than accrued interest. This is of crucial important to investors and lenders, since they often need to choose which “type” of interest to use.

**In a scenario where interest terms are few and the duration of the financial note is short, a compound interest rate is more appropriate because it’s reasonable that the lender make more money for a short loan. However, where interest terms are many and the duration of the note is long, it’s quite unreasonable to expect the borrower to pay such high absolute interest. In most cases, he/she would simply refuse!**

## Accrued Interest Calculator

You can download this accrued interest calculator for free in the Excel accompanying this article!

How to use the calculator:

- Modify the cells highlighted in blue to match the criteria of the financial note you would like to test
- In most cases, you won’t need to modify the interest per term, but if you would like to use a yearly term where interest is calculated every month, make terms equal to the number of years and interest per term equal to 12.

Remember, this calculator considers that the borrower doesn’t make any payments during the course of the financial note. It’s designed to demonstrate the effect of accrual-based interest accumulation.

## Compound Interest Calculator

Download Excel Template Here

How to use the calculator:

- Modify the cells highlighted in blue to match the criteria of the note you would like to test
- In most cases, you won’t need to modify the interest per term, but if you would like to use a yearly term where interest is calculated every month, make terms equal to the number of years and interest per term equal to 12.

Remember, this calculator assumes that the borrower doesn’t make any payments during the course of the note. It’s designed simply to help you understand the colossal effect compounding interest can have on the value of a note.

## Conclusion

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