What this calculator does
See what mortgage insurance adds to your house payment, and how long you'll have to pay it. PMI (private mortgage insurance) is a monthly fee many lenders add to a conventional loan, meaning one not backed by a government program. Enter the price, your down payment, the loan's rate and term, and the PMI rate from your lender. You'll see the monthly and yearly cost. You'll also see the payment after which you can ask to cancel it, and the payment after which it must end on its own. The total PMI paid either way is shown too.
Lenders usually require PMI when your down payment is under 20%. That's because the loan is then more than 80% of the home's value. The insurance protects the lender, not you. So it's worth knowing exactly when you can stop paying for it. Paying extra toward the loan each month brings that date closer, and the calculator shows by how much.
Where it's used
Why this math matters outside the classroom:
- Smaller down payments. Buyers putting 10% down on a $400,000 home at a 0.5% PMI rate add $150 a month to their payment.
- Planning cancellation. Homeowners find the payment at which a $360,000 loan falls to $320,000, 80% of the price, and ask to drop PMI then.
- Prepayment strategy. Borrowers see that $300 a month of extra principal cuts the PMI they pay from $14,250 to $8,400.
- Loan officer quotes. Lenders show the loan-to-value, the PMI amount and the expected removal date side by side on a quote.
- Sequence practice. Students step a loan balance forward month by month to find the first term of the sequence below a target value.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the home price and your down payment, as a percent or a dollar amount.
- Enter the mortgage rate and term. Then enter the PMI rate your lender quotes, as a percent of the loan per year.
- If you like, add an extra amount you'll pay toward the loan each month, and the loan's start date.
- Read the monthly PMI first. Then see when you can ask to remove it, when it ends on its own, and the total PMI paid. The yearly table shows your loan-to-value (the loan as a share of the home's value) going down.
What the inputs mean
- Home price
- When you buy, the original value is normally the lower of the price and the appraised value. Enter that figure. The 80% and 78% points are measured against it.
- PMI rate
- Lenders set your PMI rate from your credit score, down payment and loan type. The default of 0.5% is only an example. Use the rate on your loan estimate.
- Extra principal each month
- Extra money toward the principal (the amount you still owe) lowers your real balance. So you reach 80% sooner and can ask to cancel earlier. The automatic end date follows the original schedule, so extra payments don't move it.
- Loan start date
- The first payment is counted one month after this date.
Formula and method
loan L = price − down payment; loan-to-value = L ÷ price × 100 monthly PMI = L × PMI rate ÷ 100 ÷ 12 balance after k payments: each month, balance = balance × (1 + i) − (payment + extra), with i = rate ÷ 100 ÷ 12 request point = the first k with balance ≤ 80% × price automatic point = the first k on the original schedule with balance ≤ 78% × price, or the midpoint of the term if sooner PMI paid = monthly PMI × number of payments with PMI
In the formulas, L is the loan amount and i is the monthly interest rate. k counts the payments made so far. Monthly PMI here is a fixed percentage of the starting loan. That's the most common way monthly PMI you pay yourself is priced. It stays the same each month until it's removed.
Under US rules for conventional loans, you can ask the lender to cancel PMI once your balance reaches 80% of the original value. You need a good record of on-time payments. PMI must end on its own when the balance is scheduled to reach 78%, or halfway through the term at the latest. The calculator finds each point by walking through the payment schedule (the amortization schedule) one month at a time.
Worked example
A $400,000 home with 10% down, a 30-year loan at 6.5%, and PMI at 0.5% of the loan per year.
- Loan: $400,000 − 10% × $400,000 = $360,000, a 90% loan-to-value.
- Monthly PMI: $360,000 × 0.5% ÷ 12 = $150.00, or $1,800 a year.
- 80% of the value is $320,000. The balance first reaches it after payment 95.
- PMI paid if you cancel then: $150.00 × 95 = $14,250.
- 78% is $312,000, reached on the original schedule after payment 109, so PMI ends automatically then, after $16,350.
Result: PMI costs $150.00 a month. You can ask to cancel it after payment 95, about 7 years 11 months in, having paid $14,250. Adding $300 a month of extra principal moves that to payment 56 and cuts the total to $8,400.
Understanding the result
The total PMI figure is the real cost of a smaller down payment. Compare it with how long it would take to save the extra down payment, and what the home might cost by then.
The gap between the request point and the automatic point is money you can save just by asking. Mark the request month on a calendar. Then contact your servicer (the company you send payments to).
If the home's value goes up, some lenders will cancel PMI earlier than either point, based on a new appraisal. That depends on the lender's rules and isn't modeled here.
Assumptions and limitations
- A conventional fixed-rate loan with monthly payments, using the yearly rate ÷ 12, all made on time. Amounts aren't rounded to the cent.
- PMI is a fixed yearly percentage of the starting loan, paid monthly. It's charged on every payment up to the removal point.
- The original value is the price you enter, and the loan starts above 80% of it. Otherwise the calculator assumes no PMI.
- Other kinds of loan insurance and fees follow different rules and aren't modeled. That includes FHA mortgage insurance, VA funding fees, USDA guarantee fees, and PMI paid in one lump sum or paid by the lender.
- Canceling on request also needs a good payment history. It may also need proof that the home's value hasn't fallen. The calculator doesn't check these conditions.
- Removal based on a new appraisal or on rising home values isn't modeled.
Frequently asked questions
How much is PMI?
It depends on the rate your lender sets, which reflects your credit score and down payment. Multiply the loan by the yearly rate and divide by 12. On a $360,000 loan, every 0.1% of PMI rate adds $30 a month.
When can I get rid of PMI?
On a conventional loan, you can ask to cancel it once your balance reaches 80% of the original value. It must end on its own when the balance is scheduled to reach 78%, or halfway through the term if that comes first. In the default example, those are payments 95 and 109.
Do extra payments help remove PMI sooner?
Yes, if you ask to cancel. Extra money toward the principal lowers your balance faster, so you reach 80% sooner. On the default loan, $300 a month extra lets you ask after payment 56 instead of 95. That saves $5,850 of PMI.
Is it better to wait until I have 20% down?
Not always. PMI has a cost, but so does waiting. You pay rent in the meantime, and prices may go up. Compare the total PMI shown here with those costs over the time it would take you to save the difference.
Sources
- Consumer Financial Protection Bureau: When can I remove private mortgage insurance (PMI) from my loan? (checked 2026-10-19)
How this calculator is checked
Method: PMI as a fixed % of the starting loan; removal points from the standard amortization schedule against 80% (request, actual balance) and 78% or the midpoint (automatic, original schedule) of the original value. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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