Calculate simple interest, total and monthly payment from principal, annual rate and time in months, years or days, or solve for principal, rate or time.
Simple Interest Formula
This calculator applies a constant annual simple rate to one unchanged principal for the entered time. Interest does not earn further interest. It excludes payments, additional deposits, fees and taxes. The basic relationship is I = P * r * t:
I = P * r * t
The same relationship can be rearranged to solve for interest, principal, annual rate or time. A solved value is unique only when its denominator is nonzero:
P = I / (r * t) r = I / (P * t) t = I / (P * r)
Variables:
- I is the simple interest earned or charged
- P is the original principal
- r is the annual interest rate written as a decimal
- t is time in years
Select the value to find and enter the other three. Enter the annual rate as a percentage, such as 6 for 6%; the formula uses r = 0.06. A solved decimal rate is multiplied by 100 for its percentage display. Convert months to years by dividing by 12; entered days are divided by the selected fixed denominator, 365 or 360. Time solved in years is multiplied by 12 or the selected day denominator for its requested output unit.
The total amount after simple interest is the original principal plus the calculated interest:
A = P + I
Simple Interest Reference Table
The table below shows hypothetical simple-interest calculations for the stated times, including one year, 18 months and 90 days. These are arithmetic examples, not current rate offers. They assume an unchanged principal and rate, no compounding, payments, deposits, withdrawals, fees or taxes.
| Principal | Annual rate | Time | Interest | Total amount |
|---|---|---|---|---|
| $1,000 | 3% | 1 year | $30 | $1,030 |
| $5,000 | 4% | 1 year | $200 | $5,200 |
| $10,000 | 5% | 1 year | $500 | $10,500 |
| $25,000 | 6% | 18 months | $2,250 | $27,250 |
| $100,000 | 7% | 90 days, Actual/365 | $1,726.03 | $101,726.03 |
The CFPB explains that simple-interest auto loans use the outstanding balance, which changes as principal is repaid. Applying this calculator once to the original principal for the entire loan term does not model those payments or give an amortization schedule. Compounding, changing balances or rates, fees, taxes and contractual rounding can also change actual results. The solved annual simple rate is not an APR or APY calculation.
Example Problems
Example 1: Find the interest on a loan.
A $12,000 principal carries a 6.5% simple annual rate for 9 months. Convert 6.5% to 0.065 and 9 months to 0.75 year:
I = $12,000 * 0.065 * 0.75 = $585. The total amount due before any fees is $12,585.
Example 2: Find the annual rate.
An account earns $450 of simple interest on a $15,000 principal over 18 months. Convert 18 months to 1.5 years and rearrange the formula:
r = $450 / ($15,000 * 1.5) = 0.02, or 2% per year.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus previously credited interest. The gap grows as the rate, balance, compounding frequency, and time increase.
Should I use 360 or 365 days?
Use the convention in the contract or account disclosure. Here, Actual/365 (Fixed) uses entered days/365, even in a leap year; Actual/360 uses entered days/360. The calculator does not count dates or implement 30/360, Actual/Actual or leap-year adjustments. For the same positive principal, annual rate and entered days, dividing by 360 gives more interest than dividing by 365. See ISDA day-count definitions, section 4.16.
Can simple interest be negative?
The equation can be extended mathematically to negative rates, but this calculator does not accept negative values. Zero principal, rate or elapsed time gives zero interest. For an inverse goal with a zero denominator, zero interest leaves the unknown indeterminate; positive interest has no solution. With a positive denominator, zero interest gives a zero solved value. This is not an investment-return calculation.
