# 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.

Интерактивная версия: https://www.calcopenly.com/ru/finance/simple-interest-calculator
Тема: Финансовые калькуляторы

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.

## Входные данные

- **Основной долг**
- **Interest rate (per year)**
- **Время**
- **Time in** (варианты: Годы, Месяцы, Days)
- **Days in a year** (варианты: 365 (actual/365), 360 (banker's year))

## Результаты

- Проценты — основной результат
- Total amount
- Interest per year
- Amount if compounded yearly

## Формула

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

## Примеры с решением

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

- Основной долг: 10,000
- Interest rate (per year): 6%
- Время: 3
- Time in: Годы
- **Проценты: 1,800.00**
- **Total amount: 11,800.00**
- **Amount if compounded yearly: 11,910.16**
- Источник проверки: 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)

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

- Основной долг: 5000
- Interest rate (per year): 8%
- Время: 9
- Time in: Месяцы
- **Проценты: 300.00**
- **Total amount: 5,300.00**
- Источник проверки: 5000 × 0.08 × 9/12 by hand

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

- Основной долг: 20,000
- Interest rate (per year): 7.5%
- Время: 90
- Time in: Days
- Days in a year: 365 (actual/365)
- **Проценты: 369.86**
- Источник проверки: 20000 × 0.075 × 90/365 = 369.8630… (Python decimal)

### Same loan on a 360-day year

- Основной долг: 20,000
- Interest rate (per year): 7.5%
- Время: 90
- Time in: Days
- Days in a year: 360 (banker's year)
- **Проценты: 375.00**
- Источник проверки: 20000 × 0.075 × 90/360 by hand

### Zero rate

- Основной долг: 1000
- Interest rate (per year): 0%
- Время: 5
- Time in: Годы
- **Проценты: 0.00**
- **Total amount: 1,000.00**
- Источник проверки: Definition: no rate, no interest

## Вопросы

### 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.

### Насколько точен «Simple interest calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 5. Например, «10,000 at 6% for 3 years» проверяется по источнику 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal).

### Откуда взята методика?

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).

## Источники

- [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)

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