# 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.

Interactive version: https://www.calcopenly.com/finance/simple-interest-calculator
Subject: Finance calculators

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.

## Inputs

- **Principal**
- **Interest rate (per year)**
- **Time**
- **Time in** (options: Years, Months, Days)
- **Days in a year** (options: 365 (actual/365), 360 (banker's year))

## Results

- Interest — main result
- Total amount
- Interest per year
- Amount if compounded yearly

## Formula

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

## Worked examples

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

- Principal: 10,000
- Interest rate (per year): 6%
- Time: 3
- Time in: Years
- **Interest: 1,800.00**
- **Total amount: 11,800.00**
- **Amount if compounded yearly: 11,910.16**
- Checked against: 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal)

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

- Principal: 5000
- Interest rate (per year): 8%
- Time: 9
- Time in: Months
- **Interest: 300.00**
- **Total amount: 5,300.00**
- Checked against: 5000 × 0.08 × 9/12 by hand

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

- Principal: 20,000
- Interest rate (per year): 7.5%
- Time: 90
- Time in: Days
- Days in a year: 365 (actual/365)
- **Interest: 369.86**
- Checked against: 20000 × 0.075 × 90/365 = 369.8630… (Python decimal)

### Same loan on a 360-day year

- Principal: 20,000
- Interest rate (per year): 7.5%
- Time: 90
- Time in: Days
- Days in a year: 360 (banker's year)
- **Interest: 375.00**
- Checked against: 20000 × 0.075 × 90/360 by hand

### Zero rate

- Principal: 1000
- Interest rate (per year): 0%
- Time: 5
- Time in: Years
- **Interest: 0.00**
- **Total amount: 1,000.00**
- Checked against: Definition: no rate, no interest

## Questions

### 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.

### How accurate is the simple interest calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “10,000 at 6% for 3 years” is checked against 10000 × 0.06 × 3 by hand; 10000 × 1.06³ = 11910.16 (Python decimal).

### Where does the method come from?

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).

## Sources

- [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)

_Note: financial information, not professional advice._