The formula, in one paragraph
Start with the loan amount, the APR and the term in years. Divide the APR by 12 to get the monthly rate, multiply the years by 12 to get the number of payments, raise one plus that rate to the power of the payments, and the payment is the loan times the monthly rate times that growth factor, divided by the growth factor minus one. Six steps, all arithmetic — the worked example below shows every one.
Step 1: Find the monthly rate
The APR is an annual rate, but the payment is monthly, so the first step is to divide by 12. At 6.5% a year, the monthly rate is 6.5% divided by 12, which is 0.5417% a month, or 0.0054167 as a decimal. This is the rate that prices every payment: the first month’s interest is the loan times this rate, which is $30,000 times 0.0054167, or $162.50.
Step 2: Count the payments
The number of payments is the term in years times 12: 10 years means 120 payments. If the term is quoted in months already, use it as it stands. The count matters twice: it sets the growth factor in step 3 and the total paid in step 5. The payoff month is the first payment month plus 120 months.
Step 3: Raise one plus the rate to the power of the payments
The growth factor is one plus the monthly rate, raised to the power of the number of payments: (1 + 0.0054167) to the power of 120, which is 1.91218. A longer term makes it bigger — at 5 years it is 1.38282, at 25 years it is 5.05620 — and a higher rate makes it bigger faster.
Step 4: Work out the monthly payment
The payment is the loan times the monthly rate times the growth factor, divided by the growth factor minus one:
At the example numbers, that is $30,000 times 0.0054167 times 1.91218, divided by 1.91218 minus 1 — $162.50 times 1.91218 divided by 0.91218 — which is $340.64 a month. The division by the growth factor minus one is what spreads the loan evenly across the term.
Step 5: Work out the total paid and the interest
The total paid is the payment times the number of payments: $340.64 times 120, which is $40,877.27. The interest is the total paid minus the loan: $40,877.27 minus $30,000, which is $10,877.27 — about 36% on top of the loan. Compare offers by interest, not by the monthly payment alone.
Step 6: Read the first payment
Every payment is the same $340.64, but what it is made of changes. The first month’s interest is the loan times the monthly rate — $30,000 times 0.0054167, which is $162.50 — so the principal in the first payment is $340.64 minus $162.50, which is $178.14. The first year costs $1,885.15 of interest and the last year costs $140.36, because the balance shrinks with every payment.
Worked example: $30,000 loan, 6.5% APR, 10 years
Step 2: payments = 10 × 12 = 120.
Step 3: growth factor = (1 + 0.0054167)^120 = 1.91218.
Step 4: payment = $30,000 × 0.0054167 × 1.91218 ÷ (1.91218 − 1) = $340.64 a month.
Step 5: total paid = $340.64 × 120 = $40,877.27. Interest = $40,877.27 − $30,000 = $10,877.27.
Step 6: first payment = $162.50 interest + $178.14 principal. First-year interest $1,885.15; last-year interest $140.36.
Answer: $340.64 a month, $40,877.27 in all, $10,877.27 of interest.
What changes the payment most
The loan amount moves the payment in proportion: a $20,000 loan costs $227.10 a month and a $50,000 loan costs $567.74 a month, at the same rate and term. The rate moves the interest more than the payment: at 4.5% the payment is $310.92 a month and the interest is $7,309.83, while at 8.5% the payment is $371.96 a month and the interest is $14,634.85 — a 4-point gap is $61.04 a month but $7,325.02 of interest. The term moves them in opposite directions: 5 years costs $586.98 a month and $5,219.07 of interest, while 25 years costs $202.56 a month and $30,768.64 of interest.
Work backwards from your budget
When the budget is fixed, run the formula in reverse: the loan a payment affords is the payment times the growth factor minus one, divided by the monthly rate times the growth factor. At 6.5% for 10 years, $250 a month affords a $22,017.12 loan, $400 a month affords $35,227.40, and $500 a month affords $44,034.25. Start from the payment you can afford, not the loan you want.
Frequently asked questions
How do I calculate a student loan payment by hand?
Divide the APR by 12 for the monthly rate, multiply the years by 12 for the payments, raise one plus that rate to the power of the payments, and the payment is the loan times the monthly rate times that factor, divided by the factor minus one. On $30,000 at 6.5% for 10 years, the monthly rate is 0.5417%, the factor is 1.91218, and the payment is $340.64 a month.
How much interest will I pay on a student loan?
Multiply the payment by the months and subtract the loan. On $30,000 at 6.5% for 10 years, the total paid is $40,877.27 and the interest is $10,877.27. At 4.5% the interest is $7,309.83, and at 8.5% it is $14,634.85.
Why is most of my first payment interest?
Because the first month’s interest is the whole loan times the monthly rate: $30,000 times 0.5417% is $162.50, about half of the $340.64 payment. The first year costs $1,885.15 of interest and the last year costs $140.36, because the balance shrinks with every payment.
Does a longer term always cost more?
Yes, in interest — and less, in monthly payment. A 5-year term costs $5,219.07 of interest at $586.98 a month, and a 25-year term costs $30,768.64 of interest at $202.56 a month. Pick the shortest term whose payment fits your budget.
How much can I borrow with a $400 monthly payment?
$35,227.40 at 6.5% for 10 years. A $250 a month payment affords $22,017.12, and $500 a month affords $44,034.25, at the same rate and term.
Try it: run your own numbers through the free student loan calculator — loan amount, APR and term, with the payment, total and interest broken out.