Interest accrual refers to the accumulation of interest on a loan or investment over a period of time. As interest accrues on a loan, the borrower’s total debt grows larger over time. On an investment, interest accrual leads to growth in the total value of the investment.
In simple terms, interest accrual is the process of interest adding up and compounding on principal over the lifetime of a loan or the holding period of an investment.
How Does Interest Accrue?
Interest accrues based on the interest rate and outstanding principal balance of a loan, or the value of an investment asset. 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
More frequent compounding leads to faster accrual. Daily and monthly intervals result in the quickest accumulation. Less frequent semiannual and annual schedules have slower interest growth each year.
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.
Capitalization typically occurs at set intervals. 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
Interest Accrual Accounting
In financial accounting, interest set to accrue in the future gets booked in advance. This recognizes the upcoming costs and obligations from lending arrangements.
Accrued interest entries fall under the broader concept of accrued liabilities – expenses set to hit in the near future. Specific line items include:
- Interest Payable
- Accrued Interest Expense
- Unpaid Interest
As interest accrues based on accounting conventions without being paid, it accumulates on the balance sheet ready to expense when actually due. The interim accruals also impact earnings.
Under GAAP rules, companies cannot book interest income or expenses until earned. But expected near term accruals qualify to recognize ahead of cash flows. This matches expenses to related revenue activities.
During consolidation, the accounting system reverses previously recognized unpaid interest after payment. This prevents double counting gains or expenses when cash ultimately exchanges.
Without accrued interest tracking, financial statements and earnings would see extreme volatility around interest cash flows. Accrual accounting smooths this noise to better indicate financial health.
Interest Accrual Process Walkthrough
Let’s walk through a detailed accrual example demonstrating key calculations and impacts over time:
John takes out a $200,000 mortgage with a 30 year term at a 6% interest rate (APR), with monthly payments and compound interest
- Principal Amount = $200,000 This is the starting loan balance that interest accrues against over the full 30 years
- Interest Rate = 6% Expressed annually, divided by 12 months = 0.005 monthly rate
- Monthly Payment = $1,199 Based on a standard mortgage amortization schedule for the $200k balance, 6% rate over 30 years
- Interest Accrual Month 1: I = P x R I = $200,000 x 0.005 = $1,000 In the first month, $1,000 of interest accrues on the original principal per the above simple interest monthly formula.
- Payment Application Month 1: Interest Paid = $1,000 Principal Repaid = $199 Of the $1,199 initial payment, $1,000 covers Exact interest accrued, while remainder reduces principal.
- New Balance After Payment: $200,000 – $199 = $199,801
- Interest Accrual Month 2: I = $199,801 x 0.005 = $999 In month 2, the interest declines slightly since some principal was repaid, lowering the base accrual amount.
- Payment Application Month 2: $999 interest paid, $200 principal repaid
- Balance After Payment: $199,801 – $200 = $199,601
- Repeat process for all 360 monthly payments over full 30 year term…
Over time, the amortization structure pays more toward principal as the balance is paid down. But significant interest still accrues based on the monthly compounding.
- Total Interest Paid: $215,625 Driven by 30 years of monthly compound accruals!
This demonstrates how relatively small periodic interest costs accumulate into huge sums thanks to long term compound accrual!