Federal daily simple interest amortization with extra payments
Federal loans accrue interest daily: daily interest = balance x (rate/365) — $35,000 at 6.8% racks up $6.52 a day, $195.62 over a 30-day month. On the 10-year standard plan the payment is $402.78, and the loan costs $13,344 in total interest. Extra payments attack principal directly: $100 a month extra pays it off in 89 payments (32 months early) and saves $3,702; $200 extra finishes in 71 payments and saves $5,774. Because interest is simple, never compounded, every extra dollar stops accruing interest from the day it posts.
Payment set to your standard 10-year amount? Leave the default or click the standard button. Anything below monthly accrued interest will never pay off the loan.
| Strategy | Monthly Outlay | Payments | Payoff Time | Total Interest | Interest Saved |
|---|---|---|---|---|---|
| Standard plan (baseline) | $402.78 | 120 + $10 sweep | 10 yr 0 mo | $13,344 | — |
| +$50/month | $452.78 | 103 | 8 yr 7 mo | $11,187 | $2,157 |
| +$100/month | $502.78 | 89 | 7 yr 5 mo | $9,642 | $3,702 |
| +$200/month | $602.78 | 71 | 5 yr 11 mo | $7,570 | $5,774 |
| Biweekly half-payments (13/yr) | ~$402.78/mo equiv. | 108 | 9 yr 0 mo | $11,812 | $1,531 |
| One-time $1,000 principal payment | $402.78 | 116 | 9 yr 8 mo | $12,394 | $950 |
Simulated with daily simple interest over actual calendar months, first payment September 2026. Savings scale with rate: at 4.99% the same $100 extra saves less (less interest to avoid); at 7.9% it saves more.
| Balance | 4.5% | 6.8% | 8.05% |
|---|---|---|---|
| $10,000 | $1.23/day | $1.86/day | $2.21/day |
| $20,000 | $2.47/day | $3.73/day | $4.42/day |
| $35,000 | $4.32/day | $6.52/day | $7.72/day |
| $50,000 | $6.16/day | $9.32/day | $11.03/day |
| $75,000 | $9.25/day | $13.97/day | $16.54/day |
| $100,000 | $12.33/day | $18.63/day | $22.05/day |
Rates shown: 4.5% (older undergrad Direct loans), 6.8% (classic 2006-2012 unsubsidized rate), 8.05% (2023-24 graduate/parent PLUS territory — PLUS ran 8.05% that year). Each cell is balance x rate / 365. Waiting a month to start paying a $50,000 balance at 6.8% costs about $283 of accrued interest.
Federal student loans (Direct and FFEL) use daily simple interest. There's no compounding and no monthly rate conversion trickery: interest accrues on whatever principal you owe, each day, until a payment lands.
Daily interest = balance x (annual rate / 365). Your payment first covers all interest accrued since the last payment; the remainder reduces principal, and the next day's accrual is computed on that smaller number. The calculator simulates this over real calendar months, so you see the same day-count effects your servicer applies. The standard 10-year payment itself comes from amortization: payment = P x r / (1 − (1+r)^-120), with r = rate/12.
Enter your payoff balance from your servicer's statement (not the original disbursement), your rate, and when your next payment lands. If you're on the standard plan, the button fills in the exact 10-year payment. Then experiment: add extra monthly dollars, a one-time bonus payment, or both. The "interest saved" line compares against the standard 10-year baseline, holding your rate constant.
Take $35,000 at 6.8%, first payment September 2026. The standard payment is 35,000 x (0.068/12) / (1 − (1 + 0.068/12)^-120) = $402.78. Day one accrues $6.52 of interest; a 30-day month accrues $195.62. Each payment starts by clearing roughly $196 of interest, leaving about $207 toward principal. Over the 120-payment schedule, interest totals $13,344 (daily accrual leaves a ~$10 residue that the servicer sweeps up with a trivial final payment).
Now add $100 extra every month. The extra goes to principal immediately (federal rules require it once current-month interest is covered), so every subsequent day accrues less. The loan retires after 89 payments — January 2034 — with total interest of $9,642. That's $3,702 kept and 32 months of payments avoided.
One more: a single $1,000 principal payment today (say, a tax refund) drops the balance to $34,000, cutting 5 payments and $950 of interest. It's the cleanest illustration of how daily simple interest rewards early money most.
Two caveats. If you're on an income-driven plan chasing forgiveness (like RAP's 30-year track), extra payments reduce the forgiven amount and usually don't make sense. And if you hold both federal and private loans, extra dollars generally go furthest on the highest-rate loan first. This calculator is education, not financial advice.
On the federal standard plan, 10 years. A $35,000 balance at 6.8% has a fixed payment of $402.78, and the loan runs a 120-payment schedule. Extra payments shorten it fast: adding $100 a month pays the same loan off in 89 payments, and a $200 monthly extra finishes in 71. Income-driven plans like the new RAP stretch the term to as much as 30 years with any remaining balance forgiven.
Interest accrues each day on your current principal: daily interest = balance x (rate / 365). A $35,000 loan at 6.8% accrues $6.52 a day. Your payment covers accrued interest first, and whatever is left cuts principal. Because interest never compounds, every extra dollar reduces every future day's accrual from the day it posts. Paying earlier in the cycle also shaves a little interest since fewer days accrue before the payment lands.
For a $35,000 loan at 6.8%, $100 extra a month saves $3,702 in interest and clears the debt 32 months early; $200 extra saves $5,774 and 50 months. The guaranteed return equals your rate: 6.8% risk-free beats most savings accounts. The exception is if you're pursuing forgiveness on an income-driven plan, where paying extra just reduces what eventually gets forgiven.
On federal loans, anything beyond the current month's accrued interest goes straight to principal, and you can direct it to a specific loan. Servicers may apply extra payments to future due dates instead ('paid ahead' status), which delays the principal reduction, so tell them (in your online profile or by phone) to apply extras as a principal payment to your highest-rate loan.
The equivalent of adding 1/12 of your payment monthly: on the $35,000 example, about $33.57 a month extra pays the loan off in 108 payments instead of 120 and saves about $1,530 in interest. Biweekly half-payments do the same thing, producing 13 full payments a year and saving about $1,530 on this loan.
Rule of thumb: invest first if your expected return clearly beats your rate and you're capturing a 401k match (an instant 50-100% return); pay the loans first for rates above roughly 7%, especially private loans. In between, it's a risk preference: the loan payoff is a guaranteed return, the market isn't. This is general education, not financial advice.