# Simple interest calculator

> Calculate simple interest (I = P × r × t) and the maturity amount on a principal for a term in years, months or days.

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主题：财务计算器

Simple interest is paid only on the original principal: I = P × r × t, where r is the yearly rate as a decimal and t the time in years. A term in months is divided by 12, and a term in days by 365 (actual/365) or by 360, the banker's year some lenders and money markets use. The amount due at maturity is A = P(1 + rt).

With the defaults, 10,000 at 6% for 3 years earns 600 a year and 1,800 in total, for a maturity amount of 11,800. Compounded yearly at the same rate, the same deposit would reach 11,910.16, which is 110.16 more.

Interest here never earns interest of its own. Savings accounts and most deposits compound, so use the compound interest calculator for them; simple interest suits short loans, flat-rate quotes and interest accrued between coupon dates.

## 输入

- **本金**
- **Interest rate (per year)**
- **时间**
- **Time in** (选项：年, 月, Days)
- **Days in a year** (选项：365 (actual/365), 360 (banker's year))

## 结果

- 利息 — 主要结果
- Total amount
- Interest per year
- Amount if compounded yearly

## 公式

$$
I = P \cdot r \cdot t,\qquad A = P(1 + r t)
$$

## 计算示例

### 10,000 at 6% for 3 years

- 本金: 10,000
- Interest rate (per year): 6%
- 时间: 3
- Time in: 年
- **利息: 1,800.00**
- **Total amount: 11,800.00**
- **Amount if compounded yearly: 11,910.16**
- 核验来源：10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)

### 5,000 at 8% for 9 months

- 本金: 5000
- Interest rate (per year): 8%
- 时间: 9
- Time in: 月
- **利息: 300.00**
- **Total amount: 5,300.00**
- 核验来源：5000 × 0.08 × 9/12 by hand

### 20,000 at 7.5% for 90 days, actual/365

- 本金: 20,000
- Interest rate (per year): 7.5%
- 时间: 90
- Time in: Days
- Days in a year: 365 (actual/365)
- **利息: 369.86**
- 核验来源：20000 × 0.075 × 90/365 = 369.8630… (Python decimal)

### Same loan on a 360-day year

- 本金: 20,000
- Interest rate (per year): 7.5%
- 时间: 90
- Time in: Days
- Days in a year: 360 (banker's year)
- **利息: 375.00**
- 核验来源：20000 × 0.075 × 90/360 by hand

### Zero rate

- 本金: 1000
- Interest rate (per year): 0%
- 时间: 5
- Time in: 年
- **利息: 0.00**
- **Total amount: 1,000.00**
- 核验来源：Definition: no rate, no interest

## 常见问题

### How do you calculate simple interest?

Multiply the principal by the yearly rate and by the time in years: I = P × r × t. 10,000 at 6% for 3 years earns 10,000 × 0.06 × 3 = 1,800, so 11,800 is repaid. For a term in months, divide by 12 first: 5,000 at 8% for 9 months earns 5,000 × 0.08 × 9/12 = 300.

### How do you calculate simple interest for a number of days?

Divide the days by the day-count basis before multiplying. 20,000 at 7.5% for 90 days earns 20,000 × 0.075 × 90/365 = 369.86 on an actual/365 basis, and 375.00 on a 360-day banker's year. Excel's ACCRINTM function uses basis 3 for actual/365 and basis 2 for actual/360.

### How do you find the rate or the time from simple interest?

Rearrange I = P × r × t. The rate is r = I ÷ (P × t): earning 1,800 on 10,000 over 3 years means 1,800 ÷ 30,000 = 6% a year. The time is t = I ÷ (P × r): earning 3,000 on 10,000 at 6% takes 3,000 ÷ 600 = 5 years.

### Is simple interest better than compound interest?

For a borrower, yes; for a saver, no. Simple interest grows in a straight line, while compound interest also earns interest on interest. On 10,000 at 6%, the gap is only 110.16 after 3 years (1,800 against 1,910.16), but after 20 years simple interest totals 12,000 while yearly compounding adds 22,071.35.

### “Simple interest calculator”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：5。 例如，“10,000 at 6% for 3 years”根据10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)进行核验。

### 这种方法出自哪里？

OpenStax Prealgebra 2e — Simple Interest Applications (I = Prt); Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (simple vs compound interest); Microsoft Excel ACCRINTM function (simple interest accrued to maturity, basis 2 = actual/360, 3 = actual/365).

## 来源

- [OpenStax Prealgebra 2e — Simple Interest Applications (I = Prt)](https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications)
- Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (simple vs compound interest)
- [Microsoft Excel ACCRINTM function (simple interest accrued to maturity, basis 2 = actual/360, 3 = actual/365)](https://support.microsoft.com/en-gb/office/accrintm-function-f62f01f9-5754-4cc4-805b-0e70199328a7)

_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。_