How to Calculate Accrued Interest on a Loan

Accrued interest is the amount of interest that has accumulated on a loan over a period but has not yet been paid. This concept is significant for both borrowers and lenders. For borrowers, it’s a component of the total loan cost that grows continuously. For lenders, it signifies the revenue earned on provided funds. This article aims to clarify how to calculate accrued interest on various types of loans.

Core Components of Interest Calculation

Calculating accrued interest relies on understanding several fundamental variables. The principal is the initial sum borrowed or the remaining loan balance. As payments are made, the principal balance typically decreases, which affects future interest calculations.

The interest rate, often an Annual Percentage Rate (APR), dictates the cost of borrowing as a percentage of the principal. This annual rate must be converted to a decimal for calculations and adjusted to align with the period over which interest accrues, such as a daily or monthly rate. Interest rates can be fixed, remaining constant throughout the loan term, or variable, fluctuating based on market conditions.

The time period refers to the duration over which the interest is calculated, in days, months, or years. The unit of time used in the calculation must match the interest rate’s unit to ensure accuracy. For instance, a daily interest rate would be applied to the number of days interest has accumulated.

Calculating Accrued Interest

Accrued interest calculation depends on whether the loan uses simple or compound interest. Simple interest is straightforward, calculated only on the original principal. The formula is Principal × Rate × Time.

For example, a $10,000 loan with a 5% annual simple interest rate over 90 days: first convert the annual rate to a daily rate (0.05 / 365 days). The calculation is $10,000 × (0.05 / 365) × 90 days, resulting in approximately $123.29 in accrued interest.

Compound interest involves interest earning interest. Accrued interest is added to the principal, and subsequent calculations are based on this new, higher principal. The general formula is A = P(1 + r/n)^(nt), where ‘A’ is the total amount (principal plus interest), ‘P’ is the principal, ‘r’ is the annual interest rate (as a decimal), ‘n’ is the number of times interest is compounded per year, and ‘t’ is the time in years.

To illustrate, a $10,000 loan at a 5% annual rate, compounded monthly: ‘P’ is $10,000, ‘r’ is 0.05, and ‘n’ is 12. For one year, ‘t’ is 1. The calculation is A = $10,000(1 + 0.05/12)^(121), totaling approximately $10,511.62. Accrued interest is $511.62. More frequent compounding leads to a higher total.

Accrued Interest in Common Loan Scenarios

Accrued interest functions differently across various loan products. Mortgages often accrue interest daily on the outstanding principal balance. A portion of each monthly payment first covers interest accrued since the last payment, with the remainder reducing the principal.

Personal loans and auto loans utilize simple interest calculations or have interest pre-calculated over a fixed repayment schedule. Even with a fixed payment, the interest portion is calculated based on the declining principal balance, meaning more interest is paid early in the loan term.

Student loans have capitalization, where unpaid accrued interest is added to the principal balance, increasing the total owed. Interest can accrue on student loans even during deferment or forbearance, potentially leading to a higher loan balance when repayment begins.

Credit cards commonly use the average daily balance method for calculating interest. Interest accrues daily on any unpaid balance from previous billing cycles. This daily accrued interest can quickly add to overall debt if balances are carried over month to month.