What this calculator does
Work out your down payment, your loan amount, and how much to save each month to get there. The down payment is the part of a home's price you pay up front, and the rest is borrowed. It's usually given as a percent of the price. That percent affects the loan amount and the monthly payment. It often decides whether you pay mortgage insurance, too.
Pick which two numbers you know, and the calculator fills in the rest. You'll see the down payment in dollars and percent, the price, the loan amount and the loan-to-value ratio. That's the loan as a percent of the price. Turn on the savings plan to see how much to put aside each month to reach your down payment in time.
Where it's used
Why this math matters outside the classroom:
- Sizing a down payment. Putting 20% down on a $350,000 home takes $70,000 and leaves $280,000 to borrow.
- Monthly saving plan. Buyers find the monthly deposit that reaches a down-payment goal by a target date at a given savings rate.
- Comparing percentages. Home shoppers compare 5%, 10% and 20% down to see how each changes the cash needed and the loan amount.
- Car purchases. Car buyers decide how much to put down on a $25,000 vehicle and see the loan amount that remains.
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
- Choose what you know: the price and down %, the price and down $, or the down $ and down %.
- Enter those two numbers and read the rest, including the loan amount and loan-to-value.
- To plan your savings, tick the box. Enter what you've saved, how long until you buy and the interest rate your savings earn.
What the inputs mean
- Down payment
- Between 0% and 100%. At 100%, you're paying all cash and the loan is zero.
- Already saved
- Money you've already set aside for the down payment. It keeps earning the savings rate.
- Time until you buy
- How long until you plan to buy. Each month's deposit is made at the end of the month.
- Savings interest rate
- The yearly rate your savings earn. Interest is added monthly at the rate ÷ 12. Use 0 for cash that earns nothing.
Formula and method
down $ = price × down % ÷ 100 down % = down $ ÷ price × 100 price = down $ ÷ (down % ÷ 100) loan = price − down $; loan-to-value = loan ÷ price × 100 monthly saving = (goal − saved × (1 + r)^n) × r ÷ ((1 + r)^n − 1), with r = rate ÷ 100 ÷ 12
In the savings line, "goal" is the down payment and "saved" is what you have now. r is the monthly interest rate, and n is the number of months until you buy. The ^n means "to the power n", which is how interest builds on interest.
The first four lines are the same link between price, down payment and loan, rearranged. Loan-to-value and the down-payment percent always add up to 100%. So 20% down means an 80% loan-to-value.
The savings line is a standard formula for a series of equal monthly deposits that earn interest, solved for the deposit. Your current savings grow on their own. The monthly deposits fill whatever gap is left. At 0% interest, it's the gap divided by the number of months.
Worked example
A $350,000 home with 20% down. You have $10,000 saved, plan to buy in 3 years, and your savings earn 4% a year.
- Down payment: $350,000 × 20% = $70,000. Loan: $350,000 − $70,000 = $280,000, an 80% loan-to-value.
- Your $10,000 grows to $10,000 × (1 + 0.00333333)^36 ≈ $11,272.72 by the purchase date.
- Gap: $70,000 − $11,272.72 = $58,727.28.
- Monthly saving: $58,727.28 × 0.00333333 ÷ (1.00333333^36 − 1) ≈ $1,538.11.
Result: You need a $70,000 down payment and a $280,000 loan. Saving about $1,538.11 a month for 36 months gets you there, with $55,371.81 in deposits.
Understanding the result
A bigger down payment shrinks the loan and the monthly payment. On many conventional (non-government) loans, reaching 20% avoids mortgage insurance. A smaller one gets you into a home sooner, but costs more each month.
If the monthly saving looks out of reach, don't be discouraged. Try a longer time frame, a lower price or a smaller down-payment percent, and compare the effect on the loan.
Assumptions and limitations
- Savings earn interest monthly at the yearly rate ÷ 12, and deposits go in at the end of each month.
- The savings rate stays the same, and you don't take any money out.
- Closing costs, moving costs and cash kept in reserve aren't included in the goal.
- It ignores taxes on the interest you earn.
- Home prices may change before you buy. The goal is based on today's price.
- Minimum down payments depend on the loan program, and they aren't checked here.
Frequently asked questions
Do I need 20% down?
Not always. Many loan programs accept smaller down payments. But below 20%, conventional loans often add mortgage insurance. Check the minimum for the loan you're considering.
What is loan-to-value?
It's the loan as a percent of the home's price or appraised value. With 10% down, loan-to-value is 90%. Lenders use it to set pricing and insurance requirements.
Should I save more than the down payment?
Usually, yes. Closing costs, moving and early repairs all need cash. Many people also keep an emergency fund after buying. Add those to the goal if you want them covered.
What if my savings already cover the goal?
Then the monthly saving shows $0.00. That happens once your current savings, with interest, reach the down payment by your purchase date.
How this calculator is checked
Method: Direct proportion between price, down payment and loan; future value of an ordinary annuity with monthly compounding, solved for the deposit. 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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