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.
original_balance = 60000annual_rate = 6monthly_payment = 350payments_made = 120
- 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
Ready to run the numbers?
Open Loan Forgiveness Calculator