Student Loan Payment Calculator Formula
Understand the math behind the student loan payment calculator. Each variable explained with a worked example.
Formulas Used
Monthly Payment
monthly_payment = principal * monthly_rate * pow(1 + monthly_rate, n_payments) / (pow(1 + monthly_rate, n_payments) - 1)Total Amount Paid
total_paid = (principal * monthly_rate * pow(1 + monthly_rate, n_payments) / (pow(1 + monthly_rate, n_payments) - 1)) * n_paymentsTotal Interest Paid
total_interest = (principal * monthly_rate * pow(1 + monthly_rate, n_payments) / (pow(1 + monthly_rate, n_payments) - 1)) * n_payments - principalVariables
| Variable | Description | Default |
|---|---|---|
principal | Loan Amount ($) | 35000 |
annual_rate | Annual Interest Rate (%) | 5.5 |
term_years | Repayment Term (years) | 10 |
monthly_rate | Derived value= annual_rate / 100 / 12 | calculated |
n_payments | Derived value= term_years * 12 | calculated |
How It Works
How to Calculate Student Loan Payments
Student loan payments use the standard amortization formula.
Formula
Monthly Payment = P x r x (1+r)^n / ((1+r)^n - 1)
Where P = principal, r = monthly rate, n = total payments.
This formula ensures equal monthly payments over the life of the loan.
Worked Example
A $35,000 student loan at 5.5% interest over 10 years.
- 01Monthly rate = 5.5% / 12 = 0.004583
- 02Number of payments = 10 x 12 = 120
- 03Monthly payment = 35000 x 0.004583 x (1.004583)^120 / ((1.004583)^120 - 1) = $379.60
- 04Total paid = $379.60 x 120 = $45,552
- 05Total interest = $45,552 - $35,000 = $10,552
Frequently Asked Questions
What is the standard repayment term?
The standard federal student loan repayment term is 10 years (120 payments). Extended plans go up to 25 or 30 years.
Can I pay extra each month?
Yes, making extra payments reduces total interest and shortens the loan term. Specify that extra payments go toward principal.
What happens if I defer payments?
During deferment, interest may still accrue (on unsubsidized loans). This interest capitalizes, increasing your total balance.
Ready to run the numbers?
Open Student Loan Payment Calculator