Loan Forgiveness Calculator Formula
Understand the math behind the loan forgiveness calculator. Each variable explained with a worked example.
Formulas Used
Estimated Amount Forgiven
forgiven_amount = original_balance * pow(1 + monthly_rate, payments_made) - monthly_payment * (pow(1 + monthly_rate, payments_made) - 1) / monthly_rateTotal Amount Paid
total_paid_out = total_paidQualifying Payments Remaining
payments_remaining = max(0, 120 - payments_made)Variables
| Variable | Description | Default |
|---|---|---|
original_balance | Original Loan Balance ($) | 60000 |
annual_rate | Annual Interest Rate (%) | 6 |
monthly_payment | Monthly IDR Payment ($) | 350 |
payments_made | Qualifying Payments Made | 120 |
total_paid | Derived value= monthly_payment * payments_made | calculated |
monthly_rate | Derived value= annual_rate / 100 / 12 | calculated |
How It Works
How Public Service Loan Forgiveness Works
PSLF forgives remaining balance after 120 qualifying payments (10 years) while working for a qualifying employer.
Remaining Balance Formula
Balance after N payments = Original x (1+r)^N - Payment x ((1+r)^N - 1) / r
The remaining balance after 120 payments is the amount forgiven. Under IDR plans, payments are based on income rather than loan amount.
Worked Example
A $60,000 loan at 6% with $350/month IDR payments for 120 months.
- 01Monthly rate = 6% / 12 = 0.5%
- 02Balance growth = $60,000 x (1.005)^120 = $109,164
- 03Payments factor = $350 x ((1.005)^120 - 1) / 0.005 = $57,439
- 04Remaining balance = $109,164 - $57,439 = $51,725 (forgiven)
- 05Total paid = $350 x 120 = $42,000
Frequently Asked Questions
Who qualifies for PSLF?
You must work full-time for a qualifying employer (government, non-profit), have Direct Loans, be on an IDR plan, and make 120 qualifying payments.
Is forgiven amount taxed?
Under PSLF, the forgiven amount is NOT taxable. Under other IDR forgiveness (after 20-25 years), it may be taxable depending on current law.
What if I have not made 120 payments yet?
Keep making qualifying payments. You can track progress through the PSLF Help Tool on studentaid.gov.
Ready to run the numbers?
Open Loan Forgiveness Calculator