Reverse Mortgage Formula

Ask a loan officer for "the formula" and the answer depends entirely on which question you meant, because the two calculations happen at different moments in the life of the loan, take different inputs, and answer to different authorities.

The borrowing question is asked once, at origination, and never again. It produces a dollar ceiling — the principal limit — that determines the size of the pool available to you. Its inputs are the appraised value of the home, an FHA lending limit set by statute, the age of the youngest borrower or eligible non-borrowing spouse, and a projected long-term interest rate. Crucially, the final ingredient is not something you compute. It is looked up in a table HUD publishes and revises, built from actuarial modeling of how long loans stay outstanding and how the insurance fund performs. No amount of algebra will produce it from first principles, which is why any page claiming to hand you the exact number without consulting the current table should be treated with suspicion.

The growth question is asked continuously, every month, for as long as the loan lives. It produces a moving balance rather than a ceiling. Its inputs are only three: how much has actually been drawn, the accrual rate, and elapsed time. It is pure compound interest, and unlike the borrowing side, you genuinely can compute it yourself to the penny.

Confusing the two produces predictable errors. A borrower who assumes the principal limit is the debt is alarmed by a number they have not borrowed; a borrower who assumes an untouched line of credit is accruing interest declines to open one that would have cost nothing to hold. The most consequential confusion involves rates, because two different rates are in play. The expected rate — a long-term projection — feeds the borrowing calculation and is used exactly once. The note rate — the current rate on the loan — drives accrual and is the only one that ever touches your balance. On a fixed-rate loan they are set together and never diverge again. On an adjustable loan they part company immediately and permanently, and a projection built on the wrong one will be wrong by a wide margin over a twenty-year horizon. Our reverse mortgage interest calculator takes that rate anatomy apart in detail.

A third habit worth breaking: treating the principal limit as a fixed pool that sits waiting. On an adjustable-rate loan the undrawn portion grows over time, so the ceiling established at origination is a starting point rather than a permanent cap on availability. That growth is governed by the same exponential described further down, which is one more reason the two halves of the formula are easier to reason about once they are pulled apart. Everything below treats them as separate problems, because that is what they are.

The first half of the reverse mortgage formula is a two-term multiplication that looks trivial and hides all of its difficulty in the second term:

Principal Limit = Maximum Claim Amount × Principal Limit Factor

The Maximum Claim Amount is the easy half. It is the lesser of the appraised value of the home and the FHA lending limit for the Home Equity Conversion Mortgage program. "Lesser of" is the operative phrase and the source of most disappointment among owners of expensive homes. A property appraising at twice the lending limit does not produce twice the borrowing capacity; it produces exactly the limit, and every dollar of value above it is invisible to the calculation. The lending limit is a single national figure rather than a county-by-county one, and Congress and HUD have revised it upward repeatedly over the program's history, so the number in force is always the number for the year the loan closes: $1,249,125 for 2026 (HUD's HECM page). Owners routinely capped by it sometimes look instead at proprietary reverse mortgages, which sit outside FHA insurance and outside this formula entirely.

The Principal Limit Factor is where the arithmetic stops. It is a decimal — a share of the Maximum Claim Amount — that HUD publishes in tables and revises as its actuarial assumptions change. Three inputs select the cell:

• The age of the youngest borrower, or of an eligible non-borrowing spouse. Not the oldest, not the average — the youngest, because HUD is pricing the longest plausible duration the loan may stay outstanding.
• The expected interest rate, a long-term projection built at origination from a ten-year index plus the lender's margin, rounded to the increments the tables use.
• The program's current table, which is a policy artifact rather than a mathematical constant and has been revised more than once.

The directional logic is consistent and worth internalizing even without the numbers. An older youngest borrower raises the factor, because a shorter expected duration means less time for the balance to compound toward the home's value. A lower expected rate raises the factor, because a slower-growing balance takes longer to reach that same ceiling. Both levers are really asking one actuarial question: how likely is this debt to outrun this house before the loan comes due? Anything that answers "less likely" releases more money.

The calculator above does this lookup for you from HUD's current table (the one for case numbers assigned on or after October 2, 2017, under HUD Mortgagee Letter 2017-12, published on HUD's HECM page). It reads the row for the youngest borrower's age and the expected rate you enter, rounding the rate down to the table's nearest 1/8-point row so it never overstates the factor. As one example, the factor for age 70 at a 7% expected rate is 0.370, so a $500,000 home has a principal limit of $500,000 × 0.370 = $185,000. Because HUD can revise the table, the figure to act on is still the one a HUD-approved lender or counselor pulls from the table in force on your closing date. Whether you clear the program's threshold requirements at all is a separate gate, covered on our reverse mortgage eligibility calculator.

The second half is the one you can actually compute, and it is the ordinary compound interest equation with no payment term at all:

B = P × (1 + r)ⁿ

where B is the balance, P is the amount drawn, n is the number of months elapsed, and r is the monthly accrual rate. Compare that to a forward mortgage's payment formula and the difference is instructive: the forward equation exists to solve for a payment that will exhaust the balance in a fixed number of months, and every term in it is doing work to force the balance to zero. Strip the payment out and the equation collapses to plain exponential growth. That collapse is the reverse mortgage formula on the accrual side. Nothing more complicated is happening.

The subtlety lives entirely in r, and getting it wrong is the single most common error in do-it-yourself projections. Two charges accrue on a HECM balance every month, not one. The first is interest at the note rate. The second is the FHA's ongoing mortgage insurance premium of 0.5% annually, assessed on the outstanding balance and added to it in exactly the same way interest is. It is not a fee billed separately, not something you write a check for, and not optional — it is the premium funding the insurance that makes the loan non-recourse, and it compounds alongside the interest it sits next to. So:

r = (note rate + 0.5%) ÷ 12

A 7.25% note rate is therefore a 7.75% effective accrual rate, and r = 0.0775 ÷ 12 = 0.00645833 per month. Omitting the MIP looks like a rounding difference and is not: across twenty years on a $200,000 draw it accounts for roughly $88,700 of additional balance, as the next section shows.

Two more properties of this equation deserve attention. First, monthly compounding means the effective annual growth is slightly above the stated rate: at 7.75% nominal, the balance actually grows 8.031% per year, because each month's charge earns charges of its own. Second, on an adjustable-rate loan r is not constant — it moves with the index, within the program's caps — so any single-rate projection is a scenario rather than a forecast. Run the low end of the cap range and the high end, and treat the truth as living between them. The month-by-month version of this same curve is charted on our reverse mortgage amortization calculator.

Take a borrower who draws $200,000 at closing on a fixed-rate HECM with a 7.25% note rate. Add the 0.5% annual MIP and the effective accrual rate is 7.75%, giving a monthly r of 0.00645833. No voluntary payments are made, and the rate never moves. Applying B = P(1 + r)ⁿ at four horizons:

After five years (n = 60), the balance is $294,291.69. Accrued interest and MIP come to $94,291.69 — already nearly half again the original draw, and the gentlest stretch of the curve.

After ten years (n = 120), the balance reaches $433,038.00, with $233,038.00 of accrued charges. Note what the second five years did: they added about $138,700 where the first five added $94,300, on identical inputs. Nothing changed except the size of the base being charged.

After fifteen years (n = 180), the balance is $637,197.43 and accrued charges are $437,197.43. The accrued portion has now passed the original draw by more than a factor of two, and the debt is a little over three times what was borrowed.

After twenty years (n = 240), the balance stands at $937,609.55, of which $737,609.55 is accrued interest and MIP. The balance is 4.69 times the original draw. At this rate the debt doubles roughly every nine years — 107.7 months, precisely — which is the cleanest single way to hold the trajectory in your head.

Two comparisons put the numbers in context. Had the projection used the 7.25% note rate alone and ignored the mortgage insurance premium, the twenty-year balance would have come out at $848,911.31 — understating the real figure by $88,698.24. That is the cost of the most common modeling mistake, and it is not small. And had the borrower simply waited rather than drawing at closing, none of this would have accrued: on an adjustable-rate HECM, undrawn line-of-credit funds cost nothing while the available line itself grows at the same compounded rate. The formula is indifferent to why the money was taken; it only counts what was taken and when.

The alarming part of these figures needs its counterweight. The non-recourse guarantee, funded by the very MIP that inflates the balance, caps repayment at the home's appraised value at the time of sale. A $937,609.55 balance against a home worth $600,000 is settled for the value of the home, and FHA insurance absorbs the shortfall — neither the borrower nor the heirs owe the difference. What compounding genuinely threatens is not solvency but inheritance: the equity remaining for heirs, which is a race between this curve and the home's appreciation. Change the home value, age, rate, cash drawn or horizon in the calculator above to see how differently that race can run. It builds the starting balance from financed closing costs plus the cash you draw, and caps the cash at HUD's first-year limit, so it will reproduce this bare $200,000 example only if your home and age allow a draw that large. The program's insurance structure is laid out on our HECM reverse mortgage calculator.

The four balance figures above were computed directly from B = P(1 + r)ⁿ with P = $200,000 and r = 0.0775 ÷ 12 = 0.00645833, evaluated at n = 60, 120, 180 and 240 months. They round to the cent and can be reproduced in any spreadsheet. The 8.031% effective annual rate is (1 + r)¹² − 1; the roughly nine-year doubling time is ln(2) ÷ ln(1 + r) = 107.7 months; the $88,698.24 MIP gap is the same equation evaluated at 7.75% and 7.25% over 240 months, differenced.

The 7.25% note rate is illustrative, not a quote. Rates move constantly, and an adjustable-rate loan's accrual rate moves over the life of the loan within its caps, so a constant-rate projection is a scenario rather than a prediction. The $200,000 draw is likewise chosen for arithmetic clarity.

The structural elements are program rules rather than estimates, and they come from the government rather than from this site: the 0.5% ongoing mortgage insurance premium, the Maximum Claim Amount defined as the lesser of appraised value and the FHA lending limit, the Principal Limit Factor tables keyed to the youngest borrower's age and the expected rate, the non-recourse guarantee, and the rate caps on adjustable loans are all set out in HUD's governing documents for the FHA-insured HECM program, summarized at HUD's HECM program page. Consumer-facing explanations of the same mechanics, including the mandatory counseling requirement, are published by the Consumer Financial Protection Bureau.

The one Principal Limit Factor quoted on this page (0.370, for age 70 at a 7% expected rate) and every factor the calculator above uses come from HUD's published PLF table on HUD's HECM page. The 2% upfront and 0.5% annual premiums are set in HUD Mortgagee Letter 2017-12; the origination fee cap the calculator applies is in 24 CFR 206.31 (24 CFR part 206). The tables are revised as HUD's actuarial assumptions change, so the figure worth acting on is the one a HUD-approved lender or an independent HECM counselor pulls from the table in force on your closing date. Counseling is required before any HECM application, and it is the right place to have your own factor produced and explained.

Two simplifications in the projection are worth naming plainly. It assumes a single draw at closing rather than a line drawn down over time, which would accrue less; and it assumes a constant rate, which only a fixed-rate loan actually delivers. Both assumptions push the twenty-year figure toward the pessimistic end, which is the direction an educational example should err in.

This page is educational and is not lending, tax, investment, or estate-planning advice. Compounding math is deterministic; your loan terms, your eligibility, and your outcome are not. For the wider set of amortization and payoff tools on this site, start from the mortgage amortization calculator homepage.