Backwards Mortgage Calculator: Solve Loan, Rate or Term

A fixed-rate mortgage ties four numbers together: the amount borrowed, the rate, the number of months and the payment. Know any three and the fourth is fixed. Every mode in the backwards mortgage calculator is that same equation, solved for a different unknown. Choosing the mode is only a matter of asking which figure you do not have.

Table: the five solves this tool offers. Each one assumes a fixed rate and level monthly payments. The forward version of the same equation is explained step by step on the mortgage amortization formula page.

This is the plainest reason to run the maths in reverse: you have a payment you can live with and want to know what loan it supports. The formula discounts all 360 payments back to today at the loan's rate, and the total is the amount they can repay. At 7.24%, r is 0.0724 ÷ 12, or about 0.60333% a month. Over 360 months, (1 + r)^−360 works out to about 0.11470, so a $2,000 payment gives $2,000 × 0.88530 ÷ 0.0060333, which is $293,471.

The table below shows how far that answer moves with the rate and the term. Each extra $500 of payment adds the same amount of loan at a given rate, because the relationship is a straight line. The rate is what bends the result: one point lower at 30 years lifts the loan carried by $2,000 from $293,471 to $325,168.

Table: loan carried by each principal-and-interest payment, computed with the formula above. 7.24% and 6.60% are the Freddie Mac PMMS 30-year and 15-year averages for the week of October 29, 2026. The 6.24% and 8.24% columns are illustrations, one point either side.

The most expensive mistake in a backwards calculation is feeding it the wrong payment. The formula only knows about principal and interest. The CFPB explains that your total monthly payment typically adds costs such as homeowners insurance, taxes and possibly mortgage insurance on top of principal and interest, and that those amounts can change even when principal and interest stay the same.

Consider an illustrative budget of $2,400 a month that has to cover $400 of taxes and insurance. Entered whole at 7.24% for 30 years, the $2,400 suggests a $352,165 loan. Only $2,000 of it can actually repay a loan, and that supports $293,471. The gap of $58,694 is borrowing power that never existed.

The tool has a separate field for this: enter the full budget as the payment, then the taxes, insurance and HOA inside it, and the solve runs on what remains. Those three amounts differ by address and insurer, so take them from a Loan Estimate or a local quote.

Once the loan is known, the home price is simple addition: loan plus down payment. A $293,471 loan and a $40,000 down payment give $333,471. That number answers one narrow question, which is the price this payment can finance. It does not say whether you should spend it.

Three things can make the real ceiling lower:

• Costs tied to the price. A larger home usually brings a larger tax and insurance bill, which eats into the payment you started with. Rerun the solve after you have a figure for the specific home.
• Mortgage insurance. The CFPB says PMI can apply to a conventional loan with a down payment of less than 20 percent of the purchase price. In the example, $40,000 on $333,471 is 12%, so treat the premium as one more cost inside the payment. The calculator with PMI, taxes and insurance runs that forward.
• Closing costs. These are paid in cash and are separate from the down payment. The Loan Estimate lists the estimated total, so subtract it from your savings before you enter a down payment.

A creditor also has to assess your income and debts under Regulation Z's ability-to-repay rule, and this page does not model that. It only reverses the payment equation.

The rate is the one unknown you cannot isolate with algebra. It appears both inside and outside the power term, so no rearrangement gets r alone on one side. Every tool, Excel included, finds it by testing rates and closing in.

The test is easy to follow. Suppose a $300,000, 360-month loan has a $2,000 payment. Pick a rate, compute its payment, and compare:

Table: payments computed with the standard formula for each trial rate. Illustrative loan.

This calculator uses bisection: it starts between 0% and 100% a month, tests the midpoint, and halves the gap each round. A higher rate always means a higher payment, so there is only one answer to find and the search cannot miss it. The result here is 7.020%, and the tool then recomputes the payment at that rate to show you the check.

A rate solved this way is only as good as the payment entered. On this loan, a payment 50 cents lower gives 7.018% and 50 cents higher gives 7.023%, so a payment rounded to the nearest dollar is still fine for the first decimal place. It also gives the rate implied by the payment alone, so fees are not in it. Compare offers on the Loan Estimate, which also lists estimated closing costs.

Solving for the term has a direct formula: n = −ln(1 − r × P ÷ M) ÷ ln(1 + r). It also has a hard limit, and this is where a backwards mortgage calculator should refuse rather than return nonsense. The expression inside the logarithm must stay positive, which means the payment must be larger than one month's interest. At 7.24%, a month's interest on $300,000 is $1,810.

Table: months to repay an illustrative $300,000 at 7.24%, computed with the formula above, with the Freddie Mac PMMS rate for the week of October 29, 2026.

Near the limit, small changes do a great deal. The step from $1,900 to $2,100 removes almost 15 years and $272,146 of interest.

What to do when the inputs are impossible

When the payment is at or below the interest, the tool stops and shows what would work. In the $1,700 case it reports that $2,044.49 clears the balance in 30 years, $2,736.90 clears it in 15, and $1,700 can repay at most $249,450 over 30 years. So there are three ways forward: raise the payment, reduce the amount owed, or find a lower rate.

If the numbers came from a real loan rather than a plan, the payment you entered may be interest-only or a below-interest minimum. The CFPB describes negative amortization as a situation where the amount you owe still goes up because you are not paying enough to cover the interest, and warns you can end up owing more than the home is worth. Check the Loan Terms on your paperwork. An intentional interest-only period belongs on the interest-only mortgage calculator instead.

Backwards solves are also a quick audit of a loan you already have. The CFPB's summary of federal servicing rules says periodic statements must show the payment amount with its split among principal, interest and escrow, plus the principal you owe and your interest rate. The CFPB names two exceptions, coupon books and small servicers. A count of payments left is not on its list.

The statement mode has two directions. If you know the rate and the payments left, it gives the balance those payments repay. For an illustrative loan with a $2,000 payment, 7.24% and 300 payments left, that is $276,945.89. If you know the balance, it gives the rate: the same $2,000, 300 payments and a $276,945.89 balance return 7.240%, which confirms the calculation runs both ways.

A mismatch tells you something. With a $262,000 balance in place of $276,945.89, the implied rate jumps to 7.872%, far from the rate on the note. That does not mean the servicer is wrong. A balance lower than expected can point to past extra payments, which shorten the real payoff date, so the “payments left” you entered may be out of date. Other causes are a rate change or a loan modification. If you need the true count, run the remaining mortgage term calculator, which starts from the balance, the rate and the payment.

Excel has a built-in function for each direction, and the calculator prints the exact formula for whatever you solved. Each example below follows the argument order in Microsoft's documentation. The results listed were computed with this page's formulas, so a cell should match them to the displayed precision.

Table: Excel equivalents, with example inputs matching this page. Function syntax read from Microsoft Support, November 2026.

PV. The syntax is PV(rate, nper, pmt, [fv], [type]). Microsoft asks for consistent units, so a monthly loan takes the annual rate over 12 and the number of months. It also shows cash you pay out as negative, which is why the payment carries a minus sign and the result comes back positive.

RATE. The syntax is RATE(nper, pmt, pv, [fv], [type], [guess]). The order differs from PV, because nper comes first. The function works per period, so multiply by 12 to get the annual rate. Microsoft says RATE is calculated by iteration and returns #NUM! if results do not settle within 0.0000001 after 20 iterations, and that an omitted guess is assumed to be 10 percent. If you see #NUM!, supply a monthly guess in the sixth position: =RATE(360,-2000,300000,0,0,0.005)*12.

NPER. The syntax is NPER(rate, pmt, pv, [fv], [type]). A result of 309.58 means 309 full payments and a smaller final one, so round up to 310 when counting. Before relying on it, confirm the payment is larger than one month's interest. To go on from these formulas to a full table, follow the mortgage amortization calculator Excel guide.