How a fixed-rate loan works
Each month the lender adds one month of interest to the balance, which is the balance times the yearly rate divided by 12. Your payment then comes off. Early on, most of a payment is interest and only a little reduces the balance. As the balance falls, the interest part shrinks and the principal part grows.
Payment = L x i / (1 - (1+i)^-n), where L is the amount borrowed, i is the monthly rate (APR / 12) and n is the number of monthly payments. This is the standard amortization formula. Servicers of federal student loans charge interest daily, so their figures can differ from this monthly model by a few dollars.
A worked example
A graduate owes $30,000 at 6.8% on a ten-year plan. The payment is $345.24 a month for 120 months. The total repaid is $41,428.92, of which $11,428.92 is interest. Now add $100 a month. The payment becomes $445.24 and the loan is gone in 86 months, which is 7 years and 2 months.
| Standard | With $100 extra | |
|---|---|---|
| Monthly payment | $345.24 | $445.24 |
| Months to pay off | 120 | 86 |
| Total interest | $11,428.92 | $7,897.74 |
| Interest saved | $3,531.18 |
The extra $100 a month adds up to about $8,600 over 86 months and saves $3,531.18 of interest while finishing almost three years early. The lower the rate, the smaller that saving, so a loan at 3% gains less from extra payments than one at 9%.
Interest before repayment, and loans that never pay off
On many student loans, interest builds while the borrower is in school or in a grace period. Using round numbers, $5,000 at 10% for 18 months adds $750 of interest. If it is capitalized when repayment begins, the new balance is $5,750 and every later month charges interest on the larger amount. Use the months field and the checkbox to see both treatments.
A payment that does not cover the monthly interest never reduces the balance. On $10,000 at 24%, interest is $200 a month, so a $150 payment leaves the loan larger each month and even $200 stands still. The calculator tells you the monthly interest and the payment you need to beat it. A payment only a few cents above the interest takes so long that the calculator treats a payoff beyond 100 years as no payoff.
Mistakes to avoid
- Choosing a loan by its monthly payment alone. A longer term lowers the payment and raises total interest.
- Ignoring interest that builds while in school. It can add thousands before the first bill.
- Assuming extra money automatically goes to principal. Check how your servicer applies it; some hold it toward the next due date unless you ask for principal.
- Using the advertised rate when fees are added to the balance. The effective cost is higher than the APR alone.
- Treating the result as exact. Daily interest, rounding and payment dates shift the real figures slightly.
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