Investment
How To Calculate Simple Interest
Simple interest pays only on the original principal and never reinvests itself. That makes it the easiest interest calculation to verify by hand — and the right model for most short-term loans, bonds and treasury bills.
Quick Answer
I = P x r x t
- I
- Interest earned or owed
- P
- Principal — the original amount
- r
- Annual interest rate as a decimal (6% = 0.06)
- t
- Time in years (90 days = 90/365 = 0.2466 years)
- A
- Total amount, P + I
Simple interest equals principal times the annual rate (as a decimal) times time in years. The total to repay is principal plus interest, A = P + I = P(1 + rt). For terms shorter than a year, express time as a fraction: days / 365.
What Is Simple Interest?
Simple interest is charged or earned only on the original principal. Every period produces the same interest amount because the base never grows. Borrow $5,000 at 6% a year and each year costs $300 — in year one and in year ten alike. Nothing accumulates on top of anything else.
That behavior is exactly why simple interest survives in real contracts. Auto loans, many personal loans, short-term business credit lines and most bonds are quoted on a simple-interest basis: interest accrues on the outstanding principal at a daily rate, and as long as you pay on time there is no interest-on-interest. The lender's compensation comes from the rate, not from the compounding.
Compare that with compound interest, where each period's interest joins the principal and earns in the following period. Over a single period the two produce identical numbers. Over three years at 6% on $5,000, simple interest yields $900 while monthly compounding yields about $983. The gap widens with both rate and time — doubling the horizon roughly quadruples the simple-vs-compound difference, because the compounding effect applies to an already-growing balance.
The formula's structure explains why it is so easy to check mentally. Because t and r enter linearly, tripling the time triples the interest, and doubling the rate doubles it. Any result that does not scale proportionally contains an arithmetic error. There is no exponent to hide a mistake in.
Two conventions matter once the term is measured in days. Actual/365 divides the actual number of days by 365; actual/360 divides by 360 and is common in commercial lending and money markets, producing slightly more interest on the same stated rate. Banker's rules aside, always read which day-count the contract specifies — the difference on a large short-term facility is real money even though the rate looks identical.
What simple interest cannot do is model reinvestment. If your interest is credited back into the same account and earns thereafter, this formula understates the result. Use it when interest is paid out to you or paid off by you each period, and switch to compound interest when it is left in place.
Formula
I = P x r x t
Multiply principal by the annual decimal rate and by time in years. The units of r and t must agree: if r is annual, t is in years; convert months or days into fractions of a year.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal | currency | The starting amount borrowed or deposited. Assumes no additions or withdrawals during the term. |
| r | Annual interest rate as a decimal | decimal | Divide the quoted percentage by 100. A 6% rate is 0.06, never 6. |
| t | Time in years | years | Whole years, or a fraction: months / 12, or days / 365 (or / 360 under the actual/360 convention). |
| I | Interest amount | currency | Total interest over the whole term, not per year. |
A = P + I = P(1 + rt)
The combined form avoids computing interest separately when all you need is the final figure.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A | Final amount | currency | Principal plus all interest over the term. |
How To Calculate Simple Interest
- 1
Write the principal down as a plain number
Strip currency symbols and thousands separators. $5,000 becomes 5000. This is where spreadsheet imports most often fail, because a value pasted with its currency symbol arrives as text.
- 2
Convert the annual percentage to a decimal
Divide by 100: 6% becomes 0.06. If the quote is a monthly rate instead, multiply by 12 to annualize before using t in years — or keep the rate monthly and switch t to months. Never change only one of the two.
- 3
Express time in years
Three years stays 3. Nine months is 9 / 12 = 0.75. Ninety days is 90 / 365 = 0.24658 under actual/365, or 90 / 360 = 0.25 under actual/360. Check which convention the agreement uses.
- 4
Multiply the three numbers
I = P x r x t. For $5,000 at 0.06 for 3 years: 5000 x 0.06 x 3 = $900. Because interest is linear here, a one-year figure can also be scaled — $300 a year times three years gives the same $900.
- 5
Add principal back for the total
A = P + I gives what changes hands at the end: $5,000 + $900 = $5,900. If payments were made along the way, subtract them from this total rather than from the interest figure.
Examples
Example 1: Three-year term — $5,000 at 6% simple interest
- P
- $5,000
- r
- 6%
- t
- 3 years
| Step | Calculation | Result |
|---|---|---|
| Convert the rate | 6% ÷ 100 | 0.06 |
| First-year interest | $5,000 x 0.06 | $300.00 |
| Multiply by the term | $300.00 x 3 | $900.00 |
| Total interest | I = $5,000 x 0.06 x 3 | $900.00 |
| Total to repay | $5,000 + $900.00 | $5,900.00 |
Result: $900.00 interest; $5,900.00 total
Example 2: 90-day short term — $10,000 at 5%, actual/365
- P
- $10,000
- r
- 5%
- t
- 90 days
| Step | Calculation | Result |
|---|---|---|
| Convert days to years | 90 ÷ 365 | 0.246575 years |
| Convert the rate | 5% ÷ 100 | 0.05 |
| Apply the formula | $10,000 x 0.05 x 0.246575 | $123.29 |
| Total to repay | $10,000 + $123.29 | $10,123.29 |
Result: $123.29 interest; $10,123.29 total
Calculator
Interest
$900.00
- Total (principal + interest)
- $5,900.00
- Interest per year
- $300.00
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the Simple Interest calculator page.
Common Mistakes
Using the percentage instead of the decimal
Plugging 6 rather than 0.06 into the formula overshoots by a factor of 100. Divide by 100 first, and sanity-check against intuition: on a five-figure loan at a single-digit rate, annual interest should be three figures, not five.
Mixing months or days with an annual rate
Using t = 36 because the term is thirty-six months while keeping an annual rate charges thirty-six years' worth of interest. Convert to years, or convert the rate to monthly and keep t in months — change both or neither.
Applying simple interest to a compounding product
Savings accounts, credit cards and reinvested bonds accumulate interest on interest. Using I = Prt there understates the balance, sometimes by a large margin on long horizons. Check whether interest is paid out or credited back.
Ignoring the day-count convention on short terms
The same nominal rate produces more interest under actual/360 than actual/365 — about 90/84 = 1.4% more on a 90-day instrument. On a large facility that difference is real cash, even though the headline rate reads identically.
Subtracting interim payments from interest instead of principal
Payments made during the term reduce the outstanding principal, so future interest accrues on a smaller base. Treating them as reductions of interest already earned double-counts the benefit and overstates the remaining cost.
FAQ
What is the difference between simple and compound interest?
Simple interest applies only to the original principal, so every period produces the same interest amount. Compound interest adds interest to the balance so later periods earn more. They match exactly for one period and diverge after that.
Which real products use simple interest?
Most auto loans and many personal loans accrue simple interest on the outstanding balance. Bonds pay simple coupon interest on face value. Short-term money market instruments and commercial credit lines typically use a simple daily rate.
How do I calculate interest when the term is in days?
Divide the number of days by 365 for the ordinary convention, giving time as a fraction of a year, then use that as t. Some commercial agreements specify 360 days instead, which yields slightly more interest on the same stated rate.
Can I use I = Prt to find just the rate or just the term?
Yes. Rearranging gives r = I / (P x t) and t = I / (P x r). This is the fastest way to back out an unknown from a known interest charge, which is useful for checking whether a quoted rate matches what a statement actually charged.
Is simple interest ever better than compound interest?
It depends on which side of the transaction you are on. As a borrower you prefer simple interest, because you are never charged interest on interest. As a saver you prefer compounding, because it is what grows the balance faster.
References
- [1]Consumer Financial Protection Bureau, Truth in Lending Act — Regulation Z — https://www.consumerfinance.gov/rules-policy/regulations/1026/
- [2]OpenStax, Contemporary Mathematics, Mathematics of Money: Simple and Compound Interest — https://openstax.org/details/books/contemporary-mathematics
- [3]Corporate Finance Institute, Interest Rates: Simple and Compound — https://corporatefinanceinstitute.com/resources/accounting/interest-rates/