Student Loan Repayment Calculator Formula
Understand the math behind the student loan repayment calculator. Each variable explained with a worked example.
Formulas Used
Standard Monthly Payment
standard_payment = monthly_rate > 0 ? loan_balance * monthly_rate * pow(1 + monthly_rate, num_payments) / (pow(1 + monthly_rate, num_payments) - 1) : loan_balance / num_paymentsTotal Interest (Standard)
standard_total_interest = monthly_rate > 0 ? (loan_balance * monthly_rate * pow(1 + monthly_rate, num_payments) / (pow(1 + monthly_rate, num_payments) - 1)) * num_payments - loan_balance : 0Extended (25yr) Payment
extended_payment = monthly_rate > 0 ? loan_balance * monthly_rate * pow(1 + monthly_rate, 300) / (pow(1 + monthly_rate, 300) - 1) : loan_balance / 300Total Interest (25yr)
extended_total_interest = monthly_rate > 0 ? (loan_balance * monthly_rate * pow(1 + monthly_rate, 300) / (pow(1 + monthly_rate, 300) - 1)) * 300 - loan_balance : 0Variables
| Variable | Description | Default |
|---|---|---|
loan_balance | Total Student Loan Balance(USD) | 40000 |
interest_rate | Interest Rate(%) | 5.5 |
standard_term | Standard Repayment Term(years) | 10 |
monthly_rate | Derived value= interest_rate / 12 / 100 | calculated |
num_payments | Derived value= standard_term * 12 | calculated |
How It Works
Student Loan Repayment Options
Standard Repayment (10 years)
Fixed monthly payments. Highest payment but lowest total interest.
Extended Repayment (25 years)
Lower monthly payments but significantly more total interest.
Income-Driven Plans
Payments capped at 10-20% of discretionary income with forgiveness after 20-25 years.
Formula
M = P x r x (1+r)^n / [(1+r)^n - 1]
Where P is the loan balance, r is the monthly rate, and n is total payments.
Worked Example
$40,000 student loan at 5.5% interest.
- 01Standard (10yr): $434/month, $12,052 total interest
- 02Extended (25yr): $245/month, $33,567 total interest
- 03Standard saves $21,515 in interest
- 04Standard costs $189 more per month
Frequently Asked Questions
Which repayment plan is best?
The standard 10-year plan minimizes total cost. If you cannot afford the payment, income-driven plans protect your budget. Extended plans are a middle ground but cost significantly more over time.
Should I pay extra on student loans?
If your rate exceeds 5-6%, paying extra saves meaningful interest. For lower rates, you might earn more by investing extra money. Always specify that extra payments go toward principal, not future payments.
What about student loan forgiveness?
Public Service Loan Forgiveness (PSLF) forgives remaining balance after 120 qualifying payments while working for a qualifying employer. Income-driven plans forgive after 20-25 years, but the forgiven amount may be taxable.
Ready to run the numbers?
Open Student Loan Repayment Calculator