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How student loan payoff works

A student loan payoff has two moving parts: the scheduled payment that clears the balance over the standard term, and anything you pay above it. Owe $35,000 at 5.5 percent over 10 years and the scheduled payment is $379.84. Pay $500 a month instead and it clears in 85 payments.

Monthly payment

$379.84

10 years to clear $35,000.00 at 5.50%, over 120 payments.

Scheduled payment
$379.84
Total interest
$10,581.04
Total repaid
$45,581.04
$
%

The nominal rate the lender quotes, such as an APR. Not an effective annual rate.

yr

The fixed term a standard plan amortises the balance over. A plan that sets the payment from income has no fixed term to enter.

$

Once it reaches the balance, an extra has no interest left to cover, so all of it comes off the principal.

On this page

In short

  • On $35,000 at 5.5 percent over 10 years, the scheduled payment is $379.84. Total repaid is $45,581.04. Interest is $10,581.04.
  • Send a flat $500 instead and the loan clears in 85 months. Total repaid is $42,302.96. Interest is $7,302.96. Month one still charges $160.42 of interest.
  • Stretch the same $35,000 to 20 years and the payment falls to $240.76. Total repaid rises to $57,782.53. Interest is $22,782.53.
  • The extra above the scheduled payment is what shortens the term. A round $500 against a $379.84 schedule is applied to principal after that month's interest.
  • Plans, subsidies and forgiveness are jurisdictional. This page is the amortising balance and the extra payment. Student loans explained is the wider map.

The scheduled payment is the floor that clears the term

A standard student-loan schedule is the level-payment formula on the balance, the rate and the term. On $35,000 at 5.5 percent over 10 years, paid monthly, that payment is $379.84. Over 120 payments you repay $45,581.04. Interest is $10,581.04.

The student loan payoff calculator on this page works that schedule, then works a larger flat payment against the same balance. Principal falls only after that month's interest is taken off.

Student loans explained is the wider page: federal against private, income-driven plans, and what a subsidy does to the balance. This page is the arithmetic of a balance you are paying down.

A round \$500 against a \$379.84 schedule

Send $500 a month instead of $379.84. The loan clears in 85 months, not 120. Total repaid is $42,302.96. Interest is $7,302.96, less than the ten-year schedule. Month one still charges $160.42 of interest, because the opening balance has not moved yet.

The extra above $379.84 hits principal after interest, which is why months drop off the term rather than shaving a little off every remaining payment. How extra payments work is the same identity on a mortgage.

A longer standard term cuts the payment and raises the interest

Keep $35,000 and 5.5 percent. Stretch the standard term to 20 years. The scheduled payment falls to $240.76. Total repaid rises to $57,782.53. Interest is $22,782.53, more than double the ten-year sheet.

Income-driven plans can print a still-lower payment by design. A lower required payment is not a lower cost. It is a longer clock, unless something else (an extra payment, a subsidy, or forgiveness at a horizon the plan names) interrupts it. Type the payment you will actually send if you want the months-to-clear figure.

What this page is not doing

It is not an income-driven plan, not a forgiveness model, and not a tax deduction for student-loan interest. The three sheets are $35,000 at 5.5 percent over 10 years ($379.84, interest $10,581.04), a flat $500 (85 months, interest $7,302.96), and a 20-year schedule ($240.76, interest $22,782.53). This is educational material, not financial advice.

Worked examples

The standard plan on a \$35,000 balance

You owe $35,000 at 5.5 percent and the standard term is 10 years, paid monthly. What is the scheduled payment and what does the loan cost?

  1. Find the monthly rate: i=0.055/12=0.00458333i = 0.055/12 = 0.00458333.
  2. Count the months: n=10×12=120n = 10 \times 12 = 120.
  3. Work out the discount term: (1.00458333)−120=0.577675(1.00458333)^{-120} = 0.577675, so 1−0.577675=0.4223251 - 0.577675 = 0.422325.
  4. Apply the level payment formula: M=35000×0.004583330.422325M = 35000 \times \frac{0.00458333}{0.422325}, which is $379.84 a month.
  5. Multiply the unrounded payment by 120 months to get the total repaid: $45,581.04.
  6. Subtract the balance to isolate the interest: $45,581.04 minus $35,000.

The scheduled payment is $379.84 a month. Over 120 payments you repay $45,581.04, so the interest alone is $10,581.04.

Sending a round \$500 instead

Same $35,000 at 5.5 percent, but you send a round $500 every month instead of the scheduled $379.84. How long does it take and what does it cost?

  1. The monthly rate is unchanged at i=0.00458333i = 0.00458333, so the first month's interest is 35000×0.0045833335000 \times 0.00458333, which is $160.42.
  2. The payment clears that interest and the rest comes off the balance, so next month's interest is charged on a smaller number.
  3. Solve for the term rather than the payment: n=−ln⁡(1−0.00458333×35000/500)ln⁡(1.00458333)n = \frac{-\ln(1 - 0.00458333 \times 35000 / 500)}{\ln(1.00458333)}, which is 84.61 and rounds up to 85 payments.
  4. The 0.61 left over in that answer is what makes the last payment a short one. Payments 1 to 84 are the full $500 and the 85th collects only the remainder, so the total repaid is $42,302.96 rather than 85 times $500.
  5. Subtract the balance to isolate the interest: $42,302.96 minus $35,000.

The loan clears in 85 payments instead of 120, so it finishes 35 months early. Total repaid is $42,302.96 and the interest is $7,302.96, about 31 percent less than the $10,581.04 the standard plan costs.

The same debt stretched to 20 years

Keep the $35,000 at 5.5 percent but double the term to 20 years, which is what a longer repayment plan does to the schedule. What happens to the payment and to the interest?

  1. The monthly rate is still i=0.00458333i = 0.00458333, but now n=240n = 240.
  2. M=35000×0.004583331−(1.00458333)−240M = 35000 \times \frac{0.00458333}{1 - (1.00458333)^{-240}}, which is $240.76 a month.
  3. Multiply the unrounded payment by 240 months: $57,782.53 repaid in total.
  4. Subtract the balance to isolate the interest: $57,782.53 minus $35,000.

The payment falls to $240.76, over a third less each month, and the interest rises to $22,782.53. That is more than double the $10,581.04 the 10 year plan costs, on the same balance at the same rate.

Common questions

Does an extra payment have to be labelled extra?

The calculator treats a flat $500 as the payment that actually hits the balance each month. Whether a servicer applies an overage to principal, holds it, or advances the due date is a servicing rule, not a formula. The 85-month figure assumes every $500 reduces the balance after that month's $160.42 of interest.

Why does stretching the term cost so much more?

Because interest is charged on what is still owed, and a 20-year schedule keeps more owed for longer. The payment falls from $379.84 to $240.76. Interest rises from $10,581.04 to $22,782.53.

Is this a federal or a private loan?

Neither, specifically. It is a balance, a rate and a payment. Federal plans, subsidies and forgiveness sit on top of that arithmetic and can change the payment, the rate, or the ending. The student-loans guide is the map of those layers.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.