# Down payment calculator

> Down payment and closing costs you need, how long your savings take to reach them (or the monthly saving needed), and the PMI cost below 20% down.

Interactive version: https://www.calcopenly.com/finance/down-payment-calculator
Subject: Finance calculators

The savings target is the down payment plus closing costs, which Freddie Mac puts at 2% to 5% of the price. The time to reach it comes from growing what you have saved at your savings return, adding each month's saving, and finding the first month the balance covers the target; the other mode works out the monthly saving needed by a chosen date.

With the defaults, 10% down on a 400,000 home plus 3% closing costs is 52,000. Starting from 20,000 and saving 1,500 a month at 4%, you get there in 20 months. The 360,000 loan then carries PMI of 150 a month for 95 months, while saving for 20% down (92,000 with closing costs) takes 43 months.

PMI is estimated at a flat yearly rate of the loan until the balance is scheduled to reach 80% of the price, when a US servicer must cancel it on request (CFPB). Taxes on savings interest are not included.

## Inputs

- **I want to find** (options: Time to save, Monthly saving needed)
- **Home price**
- **Enter down payment as** (options: Percent of price, Amount)
- **Down payment**: Common minimums: 3% conventional (Fannie Mae 97% LTV options), 3.5% FHA, 0% VA. 20% avoids PMI.
- **Down payment**: Common minimums: 3% conventional (Fannie Mae 97% LTV options), 3.5% FHA, 0% VA. 20% avoids PMI.
- **Closing costs (of price)**: Freddie Mac: plan for 2% to 5% of the purchase price. Enter 0 to leave them out.
- **Saved so far**
- **Monthly saving**
- **Buy in**
- **Return on savings (per year)**: Compounded monthly; savings are added at the end of each month.
- **Mortgage rate (per year)**
- **Mortgage term**
- **PMI (per year, of loan)**: Freddie Mac: about $30 to $70 a month per $100,000 borrowed (0.36% to 0.84% a year). Charged below 20% down.
- **Home price growth while you save (per year)**

## Results

- Time to reach the target (months) — main result
- Time to reach the target
- Monthly saving needed
- Cash needed at purchase
- Down payment
- Closing costs
- Home price when you buy
- Loan amount
- Loan-to-value
- Principal and interest
- PMI per month
- Monthly payment with PMI
- Months of PMI
- Total PMI
- More needed for 20% down
- Time to save 20% down (months)

## Formula

$$
S(1+i)^{n} + C\,\frac{(1+i)^{n}-1}{i} \ge (d + c)\,P
$$

## Worked examples

### Freddie Mac example: 5% down on a 200,000 home

- I want to find: Time to save
- Home price: 200,000
- Enter down payment as: Percent of price
- Down payment: 5%
- Closing costs (of price): 0%
- Saved so far: 10,000
- Monthly saving: 500
- Return on savings (per year): 0%
- Mortgage rate (per year): 4.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.51%
- **Time to reach the target: 0 months**
- **Loan amount: 190,000.00**
- **Principal and interest: 962.70**
- **PMI per month: 80.75**
- **Monthly payment with PMI: 1,043.45**
- Checked against: Freddie Mac, Breaking down PMI: 5% down on 200,000, 30-year fixed at 4.5% → P&I 962.70, PMI 80.75 at 0.51%, total 1,043.45

### Freddie Mac example: 20% down, no PMI

- I want to find: Time to save
- Home price: 200,000
- Enter down payment as: Amount
- Down payment: 40,000
- Closing costs (of price): 0%
- Saved so far: 40,000
- Monthly saving: 1500
- Return on savings (per year): 0%
- Mortgage rate (per year): 4.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.51%
- **Loan amount: 160,000.00**
- **Principal and interest: 810.70**
- **PMI per month: 0.00**
- **Monthly payment with PMI: 810.70**
- **More needed for 20% down: not applicable**
- Checked against: Freddie Mac, Breaking down PMI: 20% down on 200,000 at 4.5% → P&I 810.70 and no PMI

### Defaults: 10% down plus 3% closing costs

- I want to find: Time to save
- Home price: 400,000
- Enter down payment as: Percent of price
- Down payment: 10%
- Closing costs (of price): 3%
- Saved so far: 20,000
- Monthly saving: 1500
- Return on savings (per year): 4%
- Mortgage rate (per year): 6.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.5%
- **Time to reach the target: 20 months**
- **Time to reach the target: 1 year 8 months**
- **Cash needed at purchase: 52,000.00**
- **PMI per month: 150.00**
- **Months of PMI: 95**
- **Total PMI: 14,250.00**
- **More needed for 20% down: 40,000.00**
- **Time to save 20% down: 43 months**
- Checked against: Python decimal month-by-month savings at 4%/12 (first month with balance ≥ 52,000 is 20; ≥ 92,000 is 43); PMI months from the amortization at 6.5% until the balance ≤ 320,000

### Zero return: whole months of saving

- I want to find: Time to save
- Home price: 300,000
- Enter down payment as: Percent of price
- Down payment: 10%
- Closing costs (of price): 0%
- Saved so far: 6000
- Monthly saving: 1000
- Return on savings (per year): 0%
- Mortgage rate (per year): 6.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.5%
- **Time to reach the target: 24 months**
- **Cash needed at purchase: 30,000.00**
- Checked against: Hand calculation: (30,000 − 6,000) ÷ 1,000 = 24 months exactly

### Monthly saving for 20% down plus closing costs in 5 years

- I want to find: Monthly saving needed
- Home price: 400,000
- Enter down payment as: Percent of price
- Down payment: 20%
- Closing costs (of price): 3%
- Saved so far: 20,000
- Buy in: 5 years
- Return on savings (per year): 4%
- Mortgage rate (per year): 6.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.5%
- **Monthly saving needed: 1,019.32**
- **Cash needed at purchase: 92,000.00**
- **PMI per month: 0.00**
- **Time to reach the target: not applicable**
- Checked against: Python decimal: (92,000 − 20,000 × (1 + 0.04/12)^60) ÷ (((1 + 0.04/12)^60 − 1) ÷ (0.04/12)) = 1,019.3229

### Already saved enough

- I want to find: Time to save
- Home price: 300,000
- Enter down payment as: Percent of price
- Down payment: 5%
- Closing costs (of price): 0%
- Saved so far: 20,000
- Monthly saving: 500
- Return on savings (per year): 4%
- Mortgage rate (per year): 6.5%
- Mortgage term: 30 years
- PMI (per year, of loan): 0.5%
- **Time to reach the target: 0 months**
- **Time to reach the target: 0 months**
- **Down payment: 15,000.00**
- Checked against: 20,000 saved already covers 5% of 300,000 (15,000), so no saving time is needed

## Questions

### How much should you put down on a house?

20% avoids private mortgage insurance on a conventional loan, which Freddie Mac requires above 80% loan-to-value. Lower minimums exist: 3% on Fannie Mae's 97% loan-to-value options, 3.5% on an FHA loan with a credit score of 580 or more, and nothing on a VA loan. On a 400,000 home that is 80,000, 12,000, 14,000 or 0, before closing costs.

### How much does PMI cost?

Freddie Mac puts it at about 30 to 70 a month for every 100,000 borrowed, or 0.36% to 0.84% of the loan a year. Its example: 5% down on a 200,000 home at 4.5% gives a 190,000 loan, 962.70 of principal and interest and 80.75 of PMI at 0.51%, for 1,043.45 a month. You can ask to cancel PMI when the balance is scheduled to reach 80% of the original value (CFPB).

### How long does it take to save for a down payment?

Divide the gap by what you save each month, then let interest shorten it. Reaching 52,000 from 20,000 at 1,500 a month takes 22 months with no interest, since 32,000 ÷ 1,500 = 21.3, and 20 months at 4% compounded monthly. If home prices rise while you save, the target moves too; enter a growth rate under More options.

### Do I need to save for closing costs as well?

Yes. Closing costs are paid at closing on top of the down payment, and Freddie Mac says to plan for 2% to 5% of the purchase price. On a 400,000 home that is 8,000 to 20,000, so 10% down plus 3% closing costs needs 52,000 in cash, not 40,000.

### Should I wait until I have 20% down?

Waiting avoids PMI but delays the purchase. With the defaults, buying at 10% down after 20 months means PMI of 150 a month for 95 months, 14,250 in all; waiting for 20% takes 43 months. If prices rise 4% a year while you save, 10% down plus closing costs grows from 52,000 to 56,059.68 and takes 23 months.

### How accurate is the down payment calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 7 worked examples whose answers come from independent sources; for example, “Freddie Mac example: 5% down on a 200,000 home” is checked against Freddie Mac, Breaking down PMI: 5% down on 200,000, 30-year fixed at 4.5% → P&I 962.70, PMI 80.75 at 0.51%, total 1,043.45.

### Where does the method come from?

Freddie Mac — Breaking down PMI (cost per $100,000 and a 5% vs 20% down example); Freddie Mac — What are closing costs and how much will I pay?; Consumer Financial Protection Bureau — When can I remove private mortgage insurance (PMI) from my loan?; Fannie Mae — 97% loan-to-value options.

## Sources

- [Freddie Mac — Breaking down PMI (cost per $100,000 and a 5% vs 20% down example)](https://myhome.freddiemac.com/buying/breaking-down-pmi)
- [Freddie Mac — What are closing costs and how much will I pay?](https://myhome.freddiemac.com/blog/homebuying/what-are-closing-costs-and-how-much-will-i-pay)
- [Consumer Financial Protection Bureau — When can I remove private mortgage insurance (PMI) from my loan?](https://www.consumerfinance.gov/ask-cfpb/when-can-i-remove-private-mortgage-insurance-pmi-from-my-loan-en-202/)
- [Fannie Mae — 97% loan-to-value options](https://singlefamily.fanniemae.com/originating-underwriting/mortgage-products/97-loan-value-options)

_Note: financial information, not professional advice._