Interest accrual refers to the accumulation of interest on a loan over a period of time. As interest accrues on a loan, the borrower’s total debt grows larger over time.
In simple terms, interest accrual is the process of interest adding up and compounding on principal over the lifetime of a loan. The borrower is obligated to pay the accrued interest (if capitalized) when paying off the loan. We will see the difference below.
How Does Interest Accrue?
Interest accrues based on the interest rate and outstanding principal balance of a loan.
Here is a closer look at how it works:
Interest Rate
The interest rate is expressed as an annual percentage rate (APR). It determines the speed at which interest accrues.
For example, a $10,000 loan with a 10% interest rate accrues interest at a rate of $1,000 per year ($10,000 x 0.10 = $1,000). With a 20% rate, the loan accrues $2,000 of interest annually ($10,000 x 0.20 = $2,000).
Compounding Frequency
In addition to the headline rate, the compounding frequency also impacts accrual. This refers to how often interest gets added to the principal amount each year.
Common compounding intervals are:
- Daily: Interest accrues every day
- Monthly: Interest is added each month
- Quarterly: Interest compounds every 3 months
- Semiannually: Twice a year interest compounding
- Annually: Interest is reinvested once per year
In the case of compounding interest, more frequent compounding leads to faster accrual because accrued interest is added to the principal. Then interest is calculated on this higher principal amount.
Amortization
For installment loans with scheduled repayments, accrual follows the amortization schedule. This outlines the breakdown of monthly payments between principal and interest.
In the beginning of the loan term, the majority of each repayment goes toward interest costs. As the balance is paid down over time, the interest portion gets smaller and more money funds reducing principal.
The amortization structure allows the lender to earn interest on the outstanding principal according to the terms until it is fully repaid. Borrowers pay growing equity while slowly reducing the interest accruals each payment.
Simple vs. Compound Interest Accrual
There are two main types of interest accrual models: simple interest and compound interest. The core difference comes down to whether interest earns additional interest or not.
Simple Interest
With simple interest lending, interest accrues on the original principal only. It does not compound and earn additional interest like the principal balance does.
Each payment period, interest accrues and is calculated against the initial amount. Additional interest does not get added to the principal to grow.
Here is the simple interest accrual formula:
Interest = Principal x Interest Rate x Time
- Principal = initial deposit or loan amount
- Rate = APR divided by number of accrual periods
- Time = length of accrual in years
Simple interest is straight linear growth relative to the timeline based on the full term and rate. For a $10,000 loan at 5% APR paid over 10 years, the accrual is:
Interest = $10,000 x 0.05 x 10 years = $5,000
It earns $500 of interest each year ($10,000 x 5%) without compounding, totaling $5,000 after the full 10 years.
The simple method does not incentivize early repayment because paying off the loan quicker does not save any money. The same total interest gets assessed either way.
Simple interest application scenarios include:
- Short term loans
- Late fee calculations
- De minimis consumer financing
- Basic savings accounts
- Retail installment credit
Overall, simple interest works best for shorter duration lending and starter savings vehicles.
Compound Interest
Under compound interest models, accrued interest gets added to the principal at the end of each period. This increases the base amount that gets applied to the interest calculation.
As the principal grows in increments thanks to reinvested interest, the accrual itself increases each period. This creates an exponential compounding effect.
The standard compound interest formula is:
A = P(1 + R/N)**NT
Where:
- A = Total Accrued Amount (principal + interest)
- P = Starting Principal
- R = Annual Interest Rate
- N = Compounding Periods per Year
- T = Total Years
Using the $10,000 example above, the accrual under 5% annually compounding interest is:
A = $10,000(1 + 0.05/1)**10 = $16,289
After 10 years, the initial principal grows to over $16,000 thanks to accumulated compound interest.
Benefits of compound accrual include:
- Exponential growth with reinvested interest
- Rewards early repayments with less total interest
- Allows adjustable rate terms over long horizons
Common compound interest vehicles include mortgages, car loans, student loans, bonds, and certificates of deposit at banks.
Interest Capitalization
Related to interest accrual on loans is a concept called capitalization. This refers to unpaid interest getting added to the principal loan balance.
Most people don’t understand the difference between accrual and capitalization.
Capitalization typically occurs at set intervals. Generally, interest is capitalized as the interest is accrued.
With federal student loans, for example, accrued interest capitalizes:
- When the grace period ends after graduation
- At the start of income-driven repayment
- Upon certain types of delinquency
By increasing the base principal, capitalization causes loans to accrue additional interest. This can result in negative amortization scenarios where the total balance grows over time despite making payments.
In effect, capitalization functions as retroactive compound interest on top of regular monthly accrual. Through this mechanism, student debt expands rapidly when payments cannot cover the new higher interest costs after capitalization events.Interest Accrual Formula Recap
Here is a quick recap of key interest accrual formulas covered:
Simple Interest
I = P x R x T
- I = Interest Amount
- P = Principal
- R = Annual Interest Rate
- T = Time in Years
*Does not compound
Compound Interest
A = P(1 + R/N)**NT
- A = Total Accrued Amount
- P = Starting Principal
- R = Annual Interest Rate
- N = Compounding Periods per Year
- T = Total Years
*Principal and interest compound
Capitalized Interest
New Principal = Original Principal + Accrued Interest
Unpaid interest gets added to principal balance, increasing base amount for interest calculations.
Common Products with Interest Accruals
| Lending Product | Interest Type | Description |
|---|---|---|
| Auto Loans | Simple Interest | Interest calculated on the outstanding principal balance. |
| Personal Loans | Simple Interest | Fixed or variable interest on remaining loan balance. |
| Payday Loans | Simple Interest | Short-term loans with high interest, often repaid in a lump sum. |
| Federal Student Loans (Subsidized) | Simple Interest | Interest covered by the government during deferment. |
| Credit Cards | Compound Interest | Interest accrues on both principal and unpaid interest if balance isn’t paid in full. |
| Private Student Loans | Compound Interest | Interest accrues on principal and unpaid interest, especially during deferment. |
| Mortgages (Some) | Compound Interest | Adjustable-rate mortgages may accrue interest on unpaid interest and principal. |
| Term Loans | Simple Interest | Business loans with fixed or variable interest rates. |
| Equipment Loans | Simple Interest | Loans for machinery, interest calculated on the outstanding balance. |
| Invoice Financing | Simple Interest | Interest charged on advance provided against invoices. |
| Merchant Cash Advances (MCAs) | Simple Interest | Factor rate applied to the original advance. |
| Business Lines of Credit (LOCs) | Compound Interest | Interest accrues on both principal and unpaid interest. |
| Business Credit Cards | Compound Interest | Interest accrues on unpaid balance, like consumer credit cards. |
| SBA Loans (Some) | Compound Interest | Certain SBA loans with revolving structures compound interest. |
| Commercial Real Estate Loans (Some) | Compound Interest | May accrue compound interest depending on the loan agreement. |
Regulations Governing Interest Accruals
There are several regulations that govern interest rate calculations (including accruals). These are in no particular order but important to consider if you are launching a lending product.
A few regulations that govern interest accruals and their disclosure:
Truth in Lending Act (TILA)
Regulation Z (12 CFR Part 1026) is administered by the Consumer Financial Protection Bureau (CFPB), this regulation requires lenders to clearly disclose the terms and conditions of loans, including interest rates, fees, and how interest accrues.
Usury Laws
State Usury Laws: Most states have their own usury laws that limit the maximum interest rate lenders can charge. Many states don’t like compound rates even if they haven’t explicitly prohibited it.
National Bank Act: Allows federally chartered banks to charge interest based on the rate allowed in the state where they are headquartered, which can preempt state usury laws in certain circumstances. Banks have more leeway in compounding rates e.g. credit cards.
Student Loan Regulations
Higher Education Act (HEA) and regulations issued by the Department of Education govern interest accrual on federal student loans. Interest rates on federal student loans are often fixed by law
Mortgage Loan Regulations
Real Estate Settlement Procedures Act (RESPA) and the Home Ownership and Equity Protection Act (HOEPA) govern aspects of interest accrual for mortgage loans, especially for high-cost mortgages.
Fair Debt Collection Practices Act (FDCPA)
FDCPA prohibits interest doesn’t accruals on charged off debt.
To keep it simple, just do daily simple interest accruals. Compounding makes life complicated.