How do you calculate student loan payments? Use the amortization formula: M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is your loan balance, r is the monthly interest rate, and n is the total number of monthly payments. For a $30,000 loan at 6.8% on the standard 10-year plan, that works out to $345/month and $11,429 in total interest. Below is the exact math, step by step, plus what happens when the rate, balance or term changes.
The formula and what each letter means
Every fixed student loan payment, federal or private, comes from one formula:
M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1)
- P = loan balance (the principal)
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of monthly payments (years × 12)
- M = the fixed monthly payment
The payment stays the same every month, but its split changes: early payments are mostly interest, late payments are mostly principal, because interest is always charged on the remaining balance.
Worked example: $30,000 at 6.8% over 10 years
Step 1 - convert to monthly terms: r = 0.068 / 12 = 0.005667, n = 10 × 12 = 120. Then (1 + r)ⁿ = 1.005667¹²⁰ ≈ 1.9701.
Step 2 - plug in: M = 30,000 × 0.005667 × 1.9701 / (1.9701 − 1) = 30,000 × 0.005667 × 2.0309 ≈ $345.24/month.
Step 3 - totals: $345.24 × 120 = $41,429 paid overall, of which $11,429 is interest. That interest number is the one people underestimate - more than a third of a year's payment goes to interest in the early years.
Do not do this by hand every time: our student loan calculator runs the same formula instantly and shows the extra-payment payoff boost too.
Why federal loans feel different: daily interest accrual
Federal student loans accrue interest daily, not monthly: daily interest = balance × rate ÷ 365. On $30,000 at 6.8%, that is about $5.59 of interest every single day - roughly $167 a month before you have paid a cent of principal. This is why an unsubsidized balance grows while you are in school, and why the balance you start repaying (P) is often bigger than what you originally borrowed.
Payment by balance and rate (10-year standard plan)
| Loan balance | 5.5% rate | 6.8% rate | |---|---|---| | $20,000 | $217/mo | $230/mo | | $30,000 | $326/mo | $345/mo | | $50,000 | $543/mo | $575/mo |
Two patterns worth noticing. First, the payment scales almost linearly with balance, so doubling the loan roughly doubles the payment. Second, 1.3 percentage points of rate costs about $19–$32/month depending on balance - on $30K, 5.5% vs 6.8% is $2,360 more interest over ten years. Rate shopping matters more than most borrowers think.
Same $30K, different terms: the interest trap
| Repayment term | Monthly payment | Total interest | |---|---|---| | 10 years (standard) | $345 | $11,429 | | 15 years | $266 | $17,935 | | 20 years | $229 | $24,960 |
Stretching to 20 years cuts the payment by $116/month but more than doubles the interest to nearly $25,000. Income-driven plans that extend to 20–25 years work the same way: relief now, a much bigger total bill later. Compare any two options with our loan comparison calculator before choosing.
Extra payments: $100/month cuts almost 3 years
Add $100/month to the $30,000 / 6.8% / 10-year loan and the math changes fast: the loan clears in 85 months (7.1 years) instead of 120, total paid drops to $37,898, and you save $3,531 in interest. Extra payments attack principal directly, which shrinks every future interest charge. Even $50/month extra makes a visible dent. Test your own number in the student loan calculator - the payoff-date shift is the most motivating number on the page.
Four things that change your payment
- Balance. Capitalized interest raises P before repayment even starts - the main reason unsubsidized federal loans cost more than their sticker amount.
- Rate. Refinancing to a lower rate is the only way to cut the payment without extending the term or losing federal protections.
- Term. Longer term = lower payment, far more interest (see the table above).
- Loan type. Federal consolidation and income-driven plans change n and sometimes r; private refinance changes r only.
Not sure where this payment fits? Check what is debt-to-income ratio to see how lenders view it, and pay off debt or invest first when you have spare cash after the minimums.
FAQ
What is the formula to calculate student loan payments?
M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1), where P is the loan balance, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. It gives the fixed monthly payment for any amortizing loan.
How much is the monthly payment on a $30,000 student loan?
About $345/month at 6.8% on the standard 10-year plan ($11,429 in total interest). At 5.5% it drops to $326/month. Use our student loan calculator for your exact rate and term.
How do I calculate student loan payments at a different interest rate?
Divide your annual rate by 12 to get r, then use the same formula. Small rate changes matter: on $30K over 10 years, 5.5% costs $326/month while 6.8% costs $345/month - $2,360 more in total interest.
Do federal student loans use the same formula?
Yes, but interest accrues daily (balance × rate ÷ 365), and subsidized loans do not accrue interest while you are in school. Unsubsidized loans capitalize that interest at repayment, which raises the starting balance the formula uses.
How much faster do extra payments pay off a student loan?
$100 extra per month on a $30,000 / 6.8% / 10-year loan clears it in 85 months instead of 120 and saves $3,531 in interest. Every extra dollar goes straight to principal.
Should I refinance my student loans to lower the payment?
Refinancing private loans at a lower rate is usually a win. Refinancing federal loans into a private loan lowers the rate but permanently gives up income-driven plans, deferment, and forgiveness options - compare total interest with the loan comparison calculator first, not just the monthly payment.
Estimates for planning only, not financial advice. Federal loan rules change; check studentaid.gov for current programs.