RAP is sold as the 'affordable' student-loan plan. The arithmetic says it is only cheaper in the middle, and never cleanly.

Next week the U.S. Department of Education is expected to begin mailing notices that start a countdown for the roughly 7.5 million borrowers still parked in the struck-down SAVE planSAVE planThe Saving on a Valuable Education plan, an income-driven repayment plan launched in 2023 that set unusually low payments; courts struck it down, and enrollees have since sat in a paused, interest-free $0 status.. Each borrower gets at least 90 days to choose a new plan, or a servicerservicerThe private company the government hires to manage your loan, collect payments, and move you between plans. drops them into the Standard or the new Tiered Standard plan by default. The notices are expected to go out in tranches, so most clocks would expire in the autumn. Opening the same day, July 1, is the headline replacement: the Repayment Assistance Plan (RAP), which the Department describes as the simpler, more affordable option.

'Affordable' is an adjective. We wanted an answer in numbers, so we rebuilt both payment formulas from their rulebooks and recomputed every figure by hand.

For a single borrower with no dependents, across what slice of the income distribution is RAP actually cheaper per month than New IBR (Income-Based Repayment), the income-driven plan it sits beside? Where do the two payment curves cross, and who lands on the losing side?

A note on which IBR. We model New IBR, which charges 10% of discretionary incomediscretionary incomeUnder IBR, your income minus a protected amount for basic living costs (150% of the federal poverty guideline); only this slice is used to set your payment. and forgives after 20 years. It is open only to people who had no federal loan balance as of July 1, 2014. Many longtime borrowers can use only Old IBROld IBRThe earlier version of Income-Based Repayment, for borrowers who already had loans before July 1, 2014; it charges a steeper 15% of discretionary income and forgives after 25 years. Many longtime borrowers can only use this version., which charges a steeper 15% of discretionary income and forgives after 25 years; against that harsher plan RAP looks better still, so modeling New IBR is the tougher, more conservative test of RAP's 'affordable' label. If RAP only barely beats the gentler IBR, that tells you the most it can claim.

The plans size your payment in fundamentally different ways, and the difference is the whole story.

New IBR shields part of your income first. It protects 150% of the federal poverty guidelinefederal poverty guidelineAn annual income figure published by the government to mark the poverty line; for 2025 it is $15,650 for a single person and rises by $5,500 for each additional household member. (for a single person in 2025 that is 150% of $15,650, or $23,475) and charges 10% of whatever is left, divided by 12 for a monthly figure. Earn below $23,475 and your payment is $0. The slice it taxes, the part above the floor, is called discretionary income. Because the floor is fixed, IBR's payment rises in a single straight line as income climbs: a ramp.

RAP shields nothing. It applies one flat percentage to your entire adjusted gross income, and that percentage steps up by a point at every $10,000 line. Earn $10,000 or less and you pay a $10 minimum. From there it is 1% of all your income up to $20,000, 2% up to $30,000, 3% up to $40,000, and so on, reaching 10% above $100,000. Crucially, the rate is flat, not marginal: cross a line and the higher rate re-rates every dollar you make, not just the dollars above the line. That is why RAP's payment does not ramp. It holds flat, then jumps: a staircase.

Plot both and the shape of the answer appears. RAP's staircase sits below IBR's ramp across most of the middle of the income range, which is the kernel of truth in the 'affordable' pitch. But the staircase pokes back above the ramp right after some of its steps, and past $80,000 it climbs above the ramp and never comes back down.

Reading the two curves against each other gives three findings: a lower edge where RAP starts winning, a couple of notches where it briefly loses inside the winning zone, and a hard upper cliff where it loses for good.

At the bottom of the income range, RAP is the more expensive plan, not the cheaper one. Anyone earning below $23,475 pays $0 under IBR but still owes RAP its 1% or 2%, subject to the $10 floor. Even just above the IBR floor, RAP stays pricier for a while: at $25,000 RAP's 2% works out to about $42 a month while IBR's thin slice of discretionary income is only about $13.

The two lines finally cross at about $29,300. Below that point a borrower is better off on IBR; above it, RAP pulls ahead. The arithmetic is simple enough to do on a napkin: in the 2% band, RAP charges 2% of income while IBR charges 10% of income above $23,475. Set those equal and the crossover falls at roughly $29,300. The people on the losing side of this edge are the lowest earners, exactly the group the 'affordable' label is most likely to reach.

At the bottom of the income range, the plan marketed as affordable is the more expensive one.

Even where RAP wins on average, the win is not continuous, because every $10,000 step briefly throws the payment above IBR before IBR's steeper slope catches back up.

Just past $30,000, RAP re-rates from 2% to 3%, lifting the monthly bill from about $50 to about $75 in a single dollar, while IBR is still only around $54. So from roughly $30,000 to about $33,500, RAP costs a little more, even though both the income just below and the income just above sit inside RAP's cheaper band. A second, wider notch opens after the $70,000 step: RAP jumps to 7% (about $408 a month) while IBR is near $388, and RAP stays a touch more expensive all the way to about $78,000 before dipping back under for the final stretch to $80,000. Inside the 'cheaper' band, in other words, there are stretches thousands of dollars wide where it is not.

These notches are modest in dollars, at most about $20 a month, but they matter for anyone whose income lands on a step. The plan's advantage is real on average and ragged in detail.

The last crossover is not a gentle notch but a cliff, and it is the sharpest feature of the whole design. At $80,000 of income RAP charges 7%, about $467 a month, a hair under IBR's $471. Add a single dollar and RAP re-rates the entire $80,001 at 8%, lifting the payment to about $533. That is a jump of roughly $66 for one dollar of extra income.

From that dollar onward RAP sits about $62 a month above IBR and never returns. As income keeps climbing the gap widens, partly because RAP keeps stepping up and partly because IBR's payment can be held down by its standard-payment capstandard-payment capAn IBR rule that never lets your income-driven payment exceed what you would owe on the fixed 10-year Standard plan; for high earners with small balances this can hold IBR below the straight 10%-of-income line., the rule that never lets an IBR bill exceed the fixed 10-year Standard amount. By $120,000 of income RAP runs roughly $200 a month more than IBR. The losing side of this edge is high earners, and unlike the lower edge there is no income high enough to climb back into RAP's favor.

The single, no-dependents case is the cleanest, but most borrowers are not single with no dependents, and family size moves the band. The two plans hand out family relief through different doors. IBR enlarges its poverty shield by $5,500 for each additional household member, which at 10% and divided by 12 is worth about $69 a month per dependent. RAP instead subtracts a flat $50 per dependent straight off the payment.

Because IBR's per-dependent relief ($69) is larger than RAP's ($50), every dependent you add helps IBR more than it helps RAP. The result: as the family grows, RAP's winning band both narrows and shifts upward. For a single filer with two dependents, the band where RAP beats IBR shrinks from roughly $29,300-to-$80,000 down to something closer to $47,000-to-$70,000.

The practical lesson is that 'is RAP cheaper for me' has no household-independent answer. The same income that makes RAP the bargain for a single person can make IBR the bargain for that person's coworker with two kids.

For the 7.5 million people getting these notices, the comparison that lands hardest is not RAP versus IBR but RAP versus what they have been paying, which for most of them is nothing. SAVE enrollees have spent months in an interest-free forbearanceforbearanceA temporary pause on loan payments; SAVE enrollees were placed in an interest-free forbearance, meaning no payments and, for a time, no interest piling up.: a $0 bill with the balance frozen. Even when SAVE was being billed normally, it was the most generous plan on the menu, shielding income up to 225% of poverty and charging only 5% above that for undergraduate debt.

Stack the four regimes for the same $50,000 single borrower and the size of the coming jolt is plain. The pause is $0. SAVE as actually billed was about $62. RAP, the cheaper of the two go-forward options at this income, is about $167, roughly 2.7 times the SAVE bill. New IBR is about $221. For these borrowers, 'affordable' is a comparison to IBR, not to the world they have been living in. The monthly number is going up no matter which plan they pick.

Everything above measures one quantity: the size of the monthly check. That is the first question most borrowers ask, but it is not the same question as 'which plan costs less over the life of the loan,' and the two can diverge sharply.

RAP carries three features that this comparison does not price. It waives unpaid interest, so a small payment never lets the balance grow. It adds a $50-a-month government match straight to principal, shrinking the original balance faster (this is a separate $50 from the per-dependent payment cut). And it forgives after 30 years. IBR forgives sooner, after 20 years for New IBR, but charges a larger slice along the way and offers no interest waiver or principal match. A borrower who pays RAP's higher monthly bill at high income may still come out behind over the full term, and a borrower with a small balance and a clear runway to payoff may find the monthly figure is the only one that matters. The honest version of the finding is that RAP is cheaper per month across a specific middle band, with frayed edges, and that whether it is cheaper overall is a different calculation that turns on balance size, career path, and time.

One group should ignore the lifetime math entirely: anyone chasing Public Service Loan Forgiveness, which cancels the balance after 10 years of qualifying work. For them a lower monthly payment is simply better, full stop, and the band where RAP wins is the band where RAP wins. For everyone else, the monthly number is where the decision starts, not where it ends.