How Federal Student Loan Interest Accrues Daily, With the Math

Federal Direct Loans charge interest every day, not once a month. The amount is your principal balance times the interest rate, divided by 365.25, then multiplied by the number of days since your last payment. Student loan servicer MOHELA calls Direct Loans "daily interest" loans, and the servicers CRI and MOHELA publish the same formula.

1. The formula

CRI gives the daily formula as (Current Principal Balance x Interest Rate) / 365.25. Multiply the result by a number of days to get the interest for that period. MOHELA puts it the same way: Daily Interest Accrual x Number of Days Since Last Payment = Monthly Interest Accrual.

CRI describes this as "simple interest," which is calculated only on the principal balance. The principal balance may include previously capitalized interest.

2. A worked example

Take a $10,000 balance at 6.8%. CRI uses these same numbers (a $10,000 Direct Unsubsidized Loan at 6.8%, $1.86 a day) in its capitalization example; the 30-day and 35-day figures below are calculated here.

• Rate factor: 0.068 divided by 365.25 = 0.00018617
• Daily interest: $10,000 x 0.00018617 = about $1.86
• Over 30 days: about $55.85
• Over 35 days: about $65.16

Paying five days later costs about $9.31 more in interest for that billing period. Because the monthly payment amount is fixed, more of that payment goes to interest and less to principal.

3. Where your payment goes

MOHELA says payments are applied first toward outstanding interest and the remainder to the principal balance. So if you send $200 after 30 days on the loan above, about $55.85 covers interest and about $144.15 reduces principal. The next month, the daily interest is computed on a slightly smaller balance.

Unpaid interest can pile up when your payment is smaller than the interest that accrues. MOHELA gives two cases: an income-driven repayment plan, where the monthly payment may be less than the interest between payments, and periods with no required payments, such as a deferment on an unsubsidized loan or forbearance.

4. What capitalization does to the math

Capitalization means unpaid interest is added to the principal balance. From then on, interest is charged on the larger balance.

CRI's example: a $10,000 unsubsidized loan at 6.8% accrues about $1.86 a day. During a six-month deferment with no payments, it accrues $340 (10,000 x 0.068 x 0.5). If that $340 capitalizes, the balance becomes $10,340, and daily interest rises to about $1.93.

That is about $0.06 more per day, or roughly $23 more over a year (340 x 0.068 = $23.12), and it continues for as long as the larger balance stays. If you pay the accrued interest before it capitalizes, the balance does not grow. CRI notes that paying accrued interest before capitalization occurs saves money in the long run.

For loans held by the U.S. Department of Education, CRI says interest capitalizes when a deferment ends on an unsubsidized loan, or when loans on an Income-Based Repayment (IBR) plan leave the plan voluntarily, are not recertified by the annual due date, or no longer qualify for a reduced payment.

5. Subsidized versus unsubsidized

MOHELA says that on subsidized loans you are not responsible for the interest that accrues while you are in school. On unsubsidized loans you are responsible for all the interest that accrues, even in school.

6. Check your own loan

1. Find the rate for each loan in your servicer account. Rates are set by federal law, differ by loan type and first disbursement date, and can differ loan to loan.
2. Divide the rate by 365.25 and multiply by the balance for one day of interest.
3. Multiply by the number of days between payments and compare it with your statement. Small differences can come from rounding.

The MOHELA page works through a $25,000 balance at 6.8%: about $4.65 per day, which it multiplies by 28 days. It shows $130.20 because it rounds the daily figure first. Without that rounding, the result is about $130.32.

7. Key takeaways

• Direct Loan interest = balance x rate / 365.25 x days since last payment.
• Payments are applied to outstanding interest first, then to principal.
• Capitalization adds unpaid interest to principal, so later interest is charged on a bigger base.
• Paying accrued interest before it capitalizes keeps the balance from growing.
• Your servicer's loan details, not a general rule, show your exact rate and balance.