# 贷款月供计算器

> 计算住房、汽车或个人贷款的月供、总利息，以及包含提前还款的逐月还款计划。

交互版本：https://www.calcopenly.com/zh/finance/emi-calculator
主题：财务计算器

EMI (equated monthly installment) is the fixed payment that clears a loan and its interest in equal monthly amounts. It is P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r the monthly rate (annual rate ÷ 12 ÷ 100) and n the number of months. Each payment first covers that month's interest on the balance still owed, and the rest repays principal.

With the default loan of 250,000 at 8.5% a year over 20 years, the EMI is 2,169.56 and total interest is 270,693.94, more than the amount borrowed. Extra monthly payments and a one-time prepayment (under More options) shorten the loan, and the schedule shows the interest they save.

The result assumes a fixed rate, a payment at the end of every month and no fees. A lender that rounds its EMI to a whole unit settles the difference in the last payment, so its final installment can differ slightly from this schedule.

## EMI formula, worked step by step

Take a 10 lakh (1,000,000) personal loan at 9% a year for 5 years.

1. Monthly rate: r = 9 ÷ 12 ÷ 100 = 0.0075.
2. Number of installments: n = 5 × 12 = 60.
3. Growth factor: (1 + r)^60 = 1.565681.
4. First month's interest: 1,000,000 × 0.0075 = 7,500.00.
5. EMI: 7,500.00 × 1.565681 ÷ (1.565681 − 1) = 20,758.36.

The first EMI therefore repays 13,258.36 of principal and leaves 986,741.64 owed. Sixty installments total 1,245,501.31, so interest comes to 245,501.31, or 24.6% of the loan.

The same formula gives the monthly payment on any fixed-rate amortizing loan, which is why US and UK lenders call it a loan payment rather than an EMI. On a US car or personal loan, the Truth in Lending disclosure must state the "total of payments" ([12 CFR 1026.18(h)](https://www.consumerfinance.gov/rules-policy/regulations/1026/18/)). Enter the note amount, rate and term here and the total payment should agree with it, apart from the lender's rounding of each payment. Selecting INR in settings switches the display to lakh and crore grouping (12,34,567); the arithmetic does not change.

## Tenure vs EMI table

EMI for every 100,000 (1 lakh) borrowed. Multiply by the loan size: a 35 lakh loan at 8.5% for 20 years is 35 × 867.82, about 30,374.

| Tenure | 7% | 8.5% | 10% | 12% | Interest at 8.5% as % of loan |
|---|---|---|---|---|---|
| 1 year | 8,652.67 | 8,721.98 | 8,791.59 | 8,884.88 | 4.7% |
| 2 years | 4,477.26 | 4,545.57 | 4,614.49 | 4,707.35 | 9.1% |
| 3 years | 3,087.71 | 3,156.75 | 3,226.72 | 3,321.43 | 13.6% |
| 5 years | 1,980.12 | 2,051.65 | 2,124.70 | 2,224.44 | 23.1% |
| 7 years | 1,509.27 | 1,583.65 | 1,660.12 | 1,765.27 | 33.0% |
| 10 years | 1,161.08 | 1,239.86 | 1,321.51 | 1,434.71 | 48.8% |
| 15 years | 898.83 | 984.74 | 1,074.61 | 1,200.17 | 77.3% |
| 20 years | 775.30 | 867.82 | 965.02 | 1,101.09 | 108.3% |
| 25 years | 706.78 | 805.23 | 908.70 | 1,053.22 | 141.6% |
| 30 years | 665.30 | 768.91 | 877.57 | 1,028.61 | 176.8% |

Doubling the tenure from 5 to 10 years cuts the EMI by about 40%. Going from 20 to 30 years cuts it by only 11% while interest rises from 108% to 177% of the loan. At 8.5%, going from 15 to 20 years lowers the EMI per lakh by 116.92, from 20 to 25 by 62.60 and from 25 to 30 by 36.31.

## Flat rate vs reducing balance rate

A flat rate charges interest on the original loan for the whole tenure: EMI = loan × (1 + flat rate × years) ÷ months. A reducing balance rate charges interest only on what is still owed, which is how this calculator works. For 2 lakh at 8% flat over 3 years, interest is 48,000 and the EMI is 248,000 ÷ 36 = 6,888.89. The reducing rate that gives the same EMI is 14.55%.

| Flat rate | Reducing rate over 1 year | Over 3 years | Over 5 years |
|---|---|---|---|
| 6% | 10.90% | 11.08% | 10.85% |
| 8% | 14.45% | 14.55% | 14.13% |
| 10% | 17.97% | 17.92% | 17.27% |
| 12% | 21.46% | 21.20% | 20.31% |
| 14% | 24.91% | 24.40% | 23.25% |

To convert any flat quote, work out its EMI with the formula above, enter the loan and tenure here, and change the rate until the EMI matches.

## Prepayment: shorter tenure or smaller EMI

A 50 lakh (5,000,000) home loan at 8.5% for 20 years has an EMI of 43,391.16 and total interest of 5,413,878.80. Suppose you prepay 5 lakh with the 36th installment. The lender will either keep the EMI and shorten the loan or keep the end date and lower the EMI:

| After prepaying 500,000 in month 36 | EMI | Loan ends after | Interest saved |
|---|---|---|---|
| Keep the EMI | 43,391.16 | 199 months | 1,319,638.61 |
| Keep the tenure | 38,749.70 | 240 months | 446,857.95 |

Keeping the EMI saves almost three times as much, because the full installment keeps going to a smaller balance, so more of each one repays principal. The calculator's one-time prepayment models that option. For the lower-EMI option, enter the balance after the prepayment (4,174,300.42) as the loan amount and the 204 remaining months as the tenure. Paying 5,000 extra with every EMI from the first month instead ends the loan after 187 months and saves 1,389,249.71.

## When a floating rate resets

When the benchmark on a floating-rate loan rises, the lender raises the EMI, extends the tenure, or both. For EMI-based floating-rate personal loans, a category that in RBI's definition covers home, education and consumer loans to individuals, the [Reserve Bank of India's 2023 circular](https://www.rbi.org.in/Scripts/NotificationUser.aspx?Id=12529&Mode=0) requires lenders to:

- explain at sanction how a rate change can alter the EMI, the tenure or both;
- let the borrower choose a higher EMI, a longer tenure or a mix at reset, and allow prepayment at any time;
- make sure a longer tenure does not cause negative amortization, where the EMI no longer covers the interest;
- send a quarterly statement showing principal and interest recovered, the EMI, the EMIs left and the annualized rate.

Offering a switch to a fixed rate at reset has been at the lender's option since 1 October 2025, when RBI replaced "shall" with "may, at its option" in the circular.

Take the 50 lakh loan without the prepayment. After 36 EMIs the balance is 4,674,300.42. If the rate then rises to 9.5%, keeping the tenure lifts the EMI by 2,874.16 to 46,265.32. Keeping the EMI adds 39 months instead, and lifetime interest becomes 7,105,740.56 rather than 6,000,207.28, 1,105,533.28 more. At 11.14%, the old EMI would no longer cover a month's interest on that balance. From that rate up, extending the tenure alone cannot absorb a rise. To model any reset, enter the outstanding balance, the new rate and the remaining months.

## Checking an EMI in a spreadsheet

Excel and Google Sheets have the same three functions. Give the rate per month and enter the money you receive as a negative number so the answer comes out positive.

- `=PMT(9%/12, 60, -1000000)` returns 20,758.36, the EMI from the first example.
- `=NPER(9.5%/12, -43391.16, 4674300.42)` returns 242.99, so after the reset above, keeping the old EMI takes 243 more installments.
- `=RATE(36, -6888.89, 200000)*12` returns 14.55%, the reducing-balance equivalent of the 8% flat quote.

## Mistakes that give the wrong EMI

- **Monthly rate entered as annual.** A loan quoted at 1% a month costs 12% a year. Entering 1 instead of 12 on the 10 lakh loan above over 5 years shows an EMI of 17,093.75 instead of 22,244.45.
- **Tenure in the wrong unit.** Use the "Tenure in" selector: 60 entered as years is a 720-month loan.
- **Ignoring fees.** Processing fees and insurance premiums added to the loan raise what you repay without changing the rate. Compare offers on the APR, which counts them.
- **Comparing a flat quote with a reducing one.** Convert with the table above first.

To see how much you can borrow for a given EMI, use the [loan affordability calculator](/zh/finance/loan-affordability-calculator). For a home loan with property tax, insurance and PMI, use the [mortgage calculator](/zh/finance/mortgage-calculator). With several loans to clear, the [debt snowball vs avalanche calculator](/zh/finance/debt-snowball-avalanche-calculator) orders them, and the [refinance calculator](/zh/finance/refinance-calculator) tests whether moving a loan to a lower rate pays for its costs.

## 输入

- **Loan amount**
- **Interest rate (per year)**
- **Tenure**
- **Tenure in** (选项：年, 月)
- **Extra payment every month**
- **One-time prepayment**
- **Prepay in month**

## 结果

- Monthly EMI — 主要结果
- Total interest
- Total payment
- Interest as % of loan
- Months to repay
- Interest saved by prepaying

## 公式

$$
EMI = \frac{P \cdot r \cdot (1+r)^n}{(1+r)^n - 1},\qquad r = \frac{\text{annual rate}}{12 \times 100}
$$

## 计算示例

### Home loan 25 lakh at 8.5% for 20 years

- Loan amount: 2,500,000
- Interest rate (per year): 8.5%
- Tenure: 20
- Tenure in: 年
- **Monthly EMI: 21,695.58**
- **Total interest: 2,706,939.40**
- 核验来源：Python decimal (50 digits) evaluation of the annuity formula

### Zero-rate loan

- Loan amount: 120,000
- Interest rate (per year): 0%
- Tenure: 12
- Tenure in: 月
- **Monthly EMI: 10,000.00**
- **Total interest: 0.00**
- 核验来源：P/n by definition

### One month at 12%

- Loan amount: 1000
- Interest rate (per year): 12%
- Tenure: 1
- Tenure in: 月
- **Monthly EMI: 1,010.00**
- **Total interest: 10.00**
- 核验来源：One month of interest at 1%: 1,000 × 1.01 = 1,010

### Car loan 30k at 6% for 5 years

- Loan amount: 30,000
- Interest rate (per year): 6%
- Tenure: 5
- Tenure in: 年
- **Monthly EMI: 579.98**
- 核验来源：Python decimal annuity formula: 579.98404…

## 常见问题

### How is EMI calculated?

Multiply the loan amount by the monthly rate r and by (1 + r)^n, then divide by (1 + r)^n − 1, where n is the number of monthly payments. For 250,000 at 8.5% over 20 years, r = 8.5 ÷ 1,200 ≈ 0.0070833 and n = 240, giving an EMI of 2,169.56. Excel's =PMT(8.5%/12, 240, -250000) returns the same amount.

### Does a longer loan tenure reduce the total interest?

No. A longer tenure lowers the EMI but increases total interest, because the balance stays high for longer. At 8.5%, a 250,000 loan over 10 years costs 3,099.64 a month and 121,957.07 in interest; over 20 years the EMI falls to 2,169.56 while interest more than doubles to 270,693.94.

### How much interest does a prepayment save?

Every prepayment goes straight to principal, so it removes all the interest that amount would have accrued. On a 250,000 loan at 8.5% over 20 years, one extra payment of 25,000 in month 12 saves 80,184.54 in interest and ends the loan 48 months early if the EMI stays the same. In India, RBI rules bar prepayment charges on floating-rate loans to individuals for non-business purposes, restated in the Pre-payment Charges on Loans Directions, 2025 for loans sanctioned or renewed from 1 January 2026.

### How much of each EMI goes to interest?

Interest is the monthly rate times the balance still owed, so the share falls with every payment. In month 1 of a 250,000 loan at 8.5%, interest is 1,770.83 of the 2,169.56 EMI and only 398.72 repays principal. On a 20-year schedule the principal portion first exceeds interest in month 143, and interest makes up 4.5% of the payments in the final year.

### What is the difference between a flat rate and a reducing balance rate?

A flat rate charges interest on the original loan amount for the whole term, while a reducing balance rate charges it only on what is still owed. A 10% flat rate over 5 years adds 50% of the loan in interest, which costs the same as a reducing balance rate of about 17.27% a year. Compare offers on the reducing balance rate or the APR.

### “贷款月供计算器”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：4。 例如，“Home loan 25 lakh at 8.5% for 20 years”根据Python decimal (50 digits) evaluation of the annuity formula进行核验。

### 这种方法出自哪里？

Microsoft Excel PMT function; Reserve Bank of India — Master Direction on interest rate on advances.

## 来源

- [Microsoft Excel PMT function](https://support.microsoft.com/office/pmt-function-0214da64-9a63-4996-bc20-214433fa6441)
- Reserve Bank of India — Master Direction on interest rate on advances

_仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。_