# 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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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.

## 입력

- **원금**
- **Interest rate (per year)**
- **시간**
- **Time in** (선택 항목: 년, 개월, Days)
- **Days in a year** (선택 항목: 365 (actual/365), 360 (banker's year))

## 결과

- 이자 — 주요 결과
- Total amount
- Interest per year
- Amount if compounded yearly

## 공식

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

## 계산 예제

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

- 원금: 10,000
- Interest rate (per year): 6%
- 시간: 3
- Time in: 년
- **이자: 1,800.00**
- **Total amount: 11,800.00**
- **Amount if compounded yearly: 11,910.16**
- 검증 출처: 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)

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

- 원금: 5000
- Interest rate (per year): 8%
- 시간: 9
- Time in: 개월
- **이자: 300.00**
- **Total amount: 5,300.00**
- 검증 출처: 5000 × 0.08 × 9/12 by hand

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

- 원금: 20,000
- Interest rate (per year): 7.5%
- 시간: 90
- Time in: Days
- Days in a year: 365 (actual/365)
- **이자: 369.86**
- 검증 출처: 20000 × 0.075 × 90/365 = 369.8630… (Python decimal)

### Same loan on a 360-day year

- 원금: 20,000
- Interest rate (per year): 7.5%
- 시간: 90
- Time in: Days
- Days in a year: 360 (banker's year)
- **이자: 375.00**
- 검증 출처: 20000 × 0.075 × 90/360 by hand

### Zero rate

- 원금: 1000
- Interest rate (per year): 0%
- 시간: 5
- Time in: 년
- **이자: 0.00**
- **Total amount: 1,000.00**
- 검증 출처: Definition: no rate, no interest

## 자주 묻는 질문

### 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”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 5. 예를 들어 “10,000 at 6% for 3 years”은 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

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).

## 출처

- [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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