# 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.

操作できるページ：https://www.calcopenly.com/ja/finance/down-payment-calculator
分野：お金の計算機

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.

## 入力

- **求めたいもの** (選択肢：Time to save, Monthly saving needed)
- **Home price**
- **Enter down payment as** (選択肢：Percent of price, Amount)
- **頭金**: Common minimums: 3% conventional (Fannie Mae 97% LTV options), 3.5% FHA, 0% VA. 20% avoids PMI.
- **頭金**: 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)**

## 結果

- Time to reach the target (months) — 主な結果
- Time to reach the target
- Monthly saving needed
- Cash needed at purchase
- 頭金
- 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)

## 計算式

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

## 計算例

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

- 求めたいもの: Time to save
- Home price: 200,000
- Enter down payment as: Percent of price
- 頭金: 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**
- 照合元：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

- 求めたいもの: Time to save
- Home price: 200,000
- Enter down payment as: Amount
- 頭金: 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: 該当なし**
- 照合元：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

- 求めたいもの: Time to save
- Home price: 400,000
- Enter down payment as: Percent of price
- 頭金: 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**
- 照合元：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

- 求めたいもの: Time to save
- Home price: 300,000
- Enter down payment as: Percent of price
- 頭金: 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**
- 照合元：Hand calculation: (30,000 − 6,000) ÷ 1,000 = 24 months exactly

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

- 求めたいもの: Monthly saving needed
- Home price: 400,000
- Enter down payment as: Percent of price
- 頭金: 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: 該当なし**
- 照合元：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

- 求めたいもの: Time to save
- Home price: 300,000
- Enter down payment as: Percent of price
- 頭金: 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**
- **頭金: 15,000.00**
- 照合元：20,000 saved already covers 5% of 300,000 (15,000), so no saving time is needed

## よくある質問

### 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.

### 「Down payment calculator」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：7。 例えば、「Freddie Mac example: 5% down on a 200,000 home」は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と照合しています。

### この計算方法の出典は何ですか？

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.

## 出典

- [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)

_計画の参考用です。金融機関、税務当局、市場は独自の丸め方、手数料、規則を適用します。契約などの前に該当機関へ金額を確認してください。_