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.
principal = 35000annual_rate = 5.5term_years = 10
- 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
Ready to run the numbers?
Open Student Loan Payment Calculator