The formula, in one paragraph
Start with the balance, the APR and the monthly payment. The month’s interest is the balance times the APR divided by 12, the payment covers the interest first and then the balance, and the payoff is the month-by-month simulation of the balance falling until it reaches zero. The bigger the payment, the more of it reaches the balance, and the faster the balance falls.
Step 1: Work out the month’s interest
The interest is the balance times the APR divided by 12, because the APR is the yearly rate and the loan charges a twelfth of it each month. At the example numbers that is $30,000 times 6.8% divided by 12, which is $170.00 of interest in month 1. At 4.5% the same balance costs only $112.50 of interest in month 1, which is $57.50 less, and at 9% it costs $225.00, which is $55.00 more.
Step 2: Work out what reaches the balance
The payment covers the interest first, so only the rest touches the balance. At $350 a month and $170.00 of interest, $180.00 reaches the balance in month 1. At $450 a month, $280.00 reaches the balance, and at $200 a month, only $30.00 does. That is why the payment matters so much: the part that reaches the balance is the part that shortens the loan.
Step 3: Simulate month by month
Each month, add the interest to the balance and subtract the payment, then work out the next month from the new balance. After month 1 the balance is $30,000 plus $170.00 minus $350.00, which is $29,820.00 — only $180.00 of the payment touched the balance. The interest shrinks with the balance, so more of the $350 payment reaches the balance every month, and the loan takes 118 months to reach zero. A bigger payment never shrinks the balance faster at the start: a $500 a month payment puts $330.00 against the balance in month 1, so the same loan takes 74 months, and a $450 a month payment takes 84 months.
Step 4: Read the totals
Add up the interest over all the months for the total interest, and add the balance for the total paid. At the example numbers the interest over 118 months is $11,188.54, and the total paid is $30,000 plus $11,188.54, which is $41,188.54 — and the last payment is $238.54, smaller than the usual $350. The standard 10-year plan is $345.24 a month with $11,428.92 of interest, so paying $350 a month saves $240.38 of interest and 2 months against it.
That box is the whole formula.
Worked example: the default loan
Step 2: balance after month 1 = $30,000 + $170.00 − $350.00 = $29,820.00.
Step 3: repeat for 118 months — interest $11,188.54, total $41,188.54.
Step 4: last payment $238.54, standard plan $345.24/mo, interest $11,428.92.
Answer: 118 months (9 yr 10 mo), $11,188.54 of interest, $41,188.54 paid in all.
What changes the payoff most
The payment moves the payoff fastest. Paying $500 a month takes 74 months and costs $6,767.26 of interest, and paying $200 a month takes 336 months and costs $37,146.82 — more in interest than the balance itself. The balance is next: a $25,000 balance takes 92 months and costs $7,134.00, and a $40,000 balance takes 185 months and costs $24,605.81. The APR is third: at 4.5% the $30,000 balance takes 104 months and costs $6,259.42, which is $4,929.12 less than at 6.8%, and at 9% it takes 138 months and costs $18,229.08.
Paying extra: the same loan, different numbers
A bigger payment and the standard plan use the same first month’s interest: $170.00 either way. The numbers part company at the payment. The standard plan is $345.24 a month and takes 120 months, with $11,428.92 of interest. Paying $350 a month takes 118 months and costs $11,188.54 — a $240.38 saving. Paying $450 a month, a hundred dollars extra, takes 84 months and costs $7,784.24, saving 34 months and $3,404.30. Paying $500 a month takes 74 months and costs $6,767.26, saving 44 months and $4,421.28. Every extra dollar goes straight to the balance, because the interest is already covered.
Work backwards from a payoff date you want
When the payoff date is fixed, run the formula in reverse. A $591.21 a month payment clears the $30,000 loan in 60 months, $345.25 a month clears it in 120 months, $266.31 a month clears it in 180 months, and $229.01 a month clears it in 240 months. At $350 a month, the biggest balance gone in 120 months is $30,413.54, and in 60 months it is $17,760.21. Check the payment against the interest first: at $350 a month and 6.8% APR, any balance above $61,764.71 never pays off, because the first month’s interest alone is more than $350. Pay more than the interest every month, or the loan never shrinks.
Frequently asked questions
How do I pay off my student loans faster?
Pay more than the minimum every month. On a $30,000 loan at 6.8% APR, $350 a month takes 118 months, and $450 a month takes 84 months — a hundred dollars extra saves 34 months and $3,404.30 of interest.
How long does it take to pay off $30,000 in student loans?
118 months — 9 years and 10 months — at $350 a month and 6.8% APR. It costs $11,188.54 of interest, for $41,188.54 paid in all. The standard 10-year plan is $345.24 a month.
How much interest will I pay on a $30,000 student loan?
$11,188.54 at 6.8% APR and $350 a month. Paying $500 a month instead costs only $6,767.26 of interest, and paying $200 a month costs $37,146.82.
What payment pays off a $30,000 student loan in 5 years?
$591.21 a month. A $591.21 a month payment clears the loan in 60 months. In 10 years it takes $345.25 a month, and in 20 years $229.01 a month.
Can a student loan never pay off?
Yes, if the payment is below the monthly interest. At $350 a month and 6.8% APR, any balance above $61,764.71 never pays off, because the first month’s interest alone is more than $350.
What if I can only pay $200 a month?
The loan takes 336 months — 28 years — and costs $37,146.82 of interest, more than the balance itself. Only $30.00 of the first payment touches the balance, because the first month’s interest is $170.00.
Try it: run your own numbers through the free student loan payoff calculator — payoff time, interest and total.