How this instrument works
An income-driven repayment (IDR) plan caps the required monthly payment at a share of discretionary income rather than at whatever amount would pay the loan off inside a fixed term. This instrument reuses the ordinary loan-amortization formula but runs it forward with that capped payment substituted in, then reports whatever remains after the plan's fixed forgiveness window closes — typically 20 or 25 years, depending on the plan and whether the debt is undergraduate or graduate.
Whether the remaining figure grows or shrinks turns on one comparison: the payment against the interest accruing that month, which equals the balance times the monthly rate. In the example below, a $100 payment on a $30,000 loan at 6% sits under the roughly $150 a month needed just to keep pace with interest, so the balance climbs for the full 20 years before anything is written off — a pattern common enough among IDR borrowers that loan servicers have a name for it: negative amortization.
The number this tool produces is the balance forgiven, not money kept. Whether a written-off balance counts as taxable income depends on the program and the tax year — federal law has excluded certain IDR discharges from taxable income at various points, and state treatment can diverge from federal treatment even then — so treat the figure as a debt erased, not automatically a tax-free windfall. It also differs mechanically from Public Service Loan Forgiveness, which discharges a balance after ten years of qualifying payments in an eligible job, tax-free, without the balance needing to grow first.
- Enter the amount owed when the plan started into Original loan balance, $.
- Set Annual interest rate, % to the rate on the loan, or a weighted average across several loans.
- Type the payment actually billed each month into Actual monthly IDR payment, $ — not what a standard term would require.
- Set Months in repayment before forgiveness to the plan's window (240 for 20 years, 300 for 25).
- Read Balance at forgiveness, $ and Amount forgiven, $ — the second is simply whatever remains of the first.
Worked example — $100 a month on a $30,000 loan
Take a $30,000 original loan balance at a 6% annual interest rate, with an actual monthly IDR payment of $100 sustained for 240 months in repayment before forgiveness. Monthly interest alone on the starting balance runs 30000 × (6 ÷ 1200) = $150 — already $50 more than the $100 payment covers, so the shortfall gets folded into principal starting with the very first month.
Running that gap forward across the full 240 months compounds it: the formula returns a balance at forgiveness of $53,102.04, well above the $30,000 originally borrowed, even though every one of those 240 payments was made on time. The amount forgiven equals that same $53,102.04 — the entire remaining balance, not merely the growth stacked on top of the original principal.
Questions
Why did my loan balance grow instead of shrink?
Because the payment income-driven repayment actually billed was smaller than the interest accruing that month. Interest equals the balance times the monthly rate; once a capped payment falls below that figure, the unpaid interest is added to principal, and next month's interest is charged on a slightly larger balance — a cycle that keeps compounding for as long as the payment stays under the interest line.
How is this different from Public Service Loan Forgiveness?
PSLF discharges the remaining balance after 120 qualifying monthly payments — ten years — in an eligible public-service job, tax-free, and never requires the balance to grow first. This instrument models the other family of programs, IDR forgiveness, which runs 20 or 25 years, applies regardless of employer, and routinely produces a forgiven balance larger than the original loan.
Is the forgiven amount taxable income?
It depends on the program and the tax year, and this instrument does not attempt to answer that — it is a policy variable, not an arithmetic one. Federal law has excluded certain IDR discharges from taxable income at points in the past; state tax treatment can diverge from federal treatment even when it does. Confirm current IRS guidance and your state's rules before treating the forgiven figure as money kept.
What payment would stop the balance from growing?
Whatever payment matches the interest accruing that month — the balance times the monthly rate. On a $30,000 loan at 6%, that threshold sits near $150 a month; pay less and the balance climbs, pay more and it heads down like an ordinary amortizing loan, just slowly, since the payment is still set by income rather than by the loan's size.
Does the calculator assume my income stays fixed?
Yes — it holds Actual monthly IDR payment, $ constant for the whole window, which is a simplification. Real IDR payments are recalculated at each annual recertification as income and family size change, so an actual balance path zig-zags around the smooth curve this formula draws. Re-run the sheet with a new payment figure whenever income changes materially.
Why reuse the same formula as a standard loan payment?
Because the relationship between balance, rate, payment, and time is identical in both cases; this instrument simply solves it for the ending balance given a fixed payment, rather than solving for the payment given an ending balance of zero. The arithmetic does not know the payment was set by an income formula instead of a loan term — it only compounds whatever figure it is given.
References
- CFPB — Student loan repayment and forgiveness tools
- Federal Student Aid — Income-Driven Repayment Plans
- IRS — Topic no. 431, Canceled Debt: Is It Taxable?
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.