Simple Interest Calculator

Interest is what you pay to borrow money, or what you are paid for lending it. You pay it on a car loan or a credit card balance, and you earn it on money sitting in a savings account or a certificate of deposit. This calculator handles the simplest version of it, and solves for whichever figure you are missing: the end balance, the principal, the rate, or the term.

What simple interest is

Simple interest is charged on the original sum alone, the principal, and nothing else. The rate is usually fixed for the life of the loan. However often the interest is worked out, it always applies to that same starting figure, so interest already added never earns interest of its own. That single rule is what separates it from compounding, and it is why a simple-interest balance grows in a straight line rather than a curve.

The formula

The whole thing fits in one line:

Simple interest = principal × rate × time

Give the calculator any three of those and it returns the fourth.

Working in years: I = Prt

Written out with symbols, the same formula is I = Prt, where:

• I is the total simple interest
• P is the principal, the original balance
• r is the annual interest rate
• t is the term in years

Because t is measured in years, a partial year is just a fraction. Six months is t = 0.5, and three months is t = 0.25.

Working in periods: I = Prn

The same idea rewritten for any frequency is I = Prn, where:

• I is the total interest
• P is the principal
• r is the rate per period
• n is the number of periods

Use this version when the rate is quoted per month or per day rather than per year. Feed in the monthly rate as r and the number of months as n, and the answer comes out in the same units you started with. The rate and the period have to match; a monthly rate with a count of years is the most common way to get an answer that is off by a factor of twelve.

Two worked examples

Take a $10,000 loan at 5% annual simple interest, repaid over five years. Multiply the principal by the annual rate: $10,000 × 0.05 = $500 a year. Multiply that by the term: $500 × 5 = $2,500 of total interest. Add it to the principal and the loan repays $12,500 in total. Divide the $500 by 12 or 365 and you have the monthly or daily interest.

Now the per-period version. With a monthly rate of 5% over one year, the interest is $10,000 × 0.05 × 12 = $6,000, so the total repayment is $16,000. Same formula, different units, and a much larger number, which is a good reminder to check whether a quoted rate is annual or monthly before signing anything.

Where simple interest actually shows up

As a borrower, simple interest is the one you want, since you only ever pay on the original balance. It turns up on some short-term loans, and on many car loans, where interest accrues daily on the outstanding principal.

As a saver or investor, the same property works against you: money that does not compound gives up the growth-on-growth that does the heavy lifting over long periods. Some assets still pay this way because it is straightforward. A bond pays a fixed coupon on its face value, and a stock pays a dividend, and neither one automatically grows the base amount. To get compounding out of them, you have to reinvest the payments as new principal yourself. Most checking accounts, savings accounts, and credit cards, by contrast, run on compound interest.

Why a loan statement may not match this figure

A simple-interest loan that you repay in instalments behaves differently from one repaid in a single lump at the end. Car loans are the usual example: interest accrues daily on whatever principal is still outstanding, and each monthly payment covers that accrued interest first, with the remainder cutting the balance. Because the balance shrinks every month, the interest charged shrinks with it, and the total ends up below the flat I = Prt figure for the same rate and term. Paying a few days early reduces it further, and paying late means more days of accrual. Use this page for the flat calculation, and the Auto Loan Calculator or Amortization Calculator when payments are spread across the term.

Simple interest against compound interest

Compound interest charges on the starting sum plus whatever interest has already piled up, so you pay interest on interest. Over a long enough run that costs a borrower more and earns an investor more.

The compound formula is:

A = P × (1 + r/n)^nt

• A is the ending balance
• P is the principal
• r is the annual interest rate as a decimal
• n is the number of times interest compounds per year
• t is the time in years

The compounding schedule matters. Monthly and annual are the most common; enter 12 for monthly and 365 for daily. The more often it compounds, the more interest changes hands. Working it out by hand gets tedious quickly, because the balance has to be recalculated every single period, which is what our Compound Interest Calculator is for.

Which one is better for you

It depends entirely on which side of the loan you are standing on. Borrowing on simple interest costs you less; saving or investing with compounding earns you more.

Put numbers on it with that same $10,000 at 5% over five years. On simple interest the total is $12,500, being $10,000 of principal plus $2,500 of interest. Compounded monthly, the same loan repays $12,833.59, or $10,000 plus $2,833.59 of interest. The $333.59 gap looks minor over five years. Stretch it to twenty and the compound figure reaches $27,126.40 against $20,000 for simple interest, because the curve keeps steepening while the straight line never does. The chart above plots both paths for the numbers you enter. For the compounding side of the comparison, our Interest Calculator and Savings Calculator carry it further.

How the year is counted

The formula needs a value for time, and lenders do not all count a year the same way. Three conventions cover most of it: 30/360 treats every month as 30 days and the year as 360, actual/365 counts real days against a 365-day year, and actual/360 counts real days against 360.

The gap is small per period and constant over time. On $10,000 at 6% for 90 days, 30/360 gives $150.00, actual/365 gives $147.95, and actual/360 gives $150.00 as well while charging for every real day, which is why it works out dearer over a full year. Actual/360 is standard in commercial lending and is one reason a business loan costs slightly more than its stated rate suggests.

Simple interest on a car loan

Most US auto loans are simple interest loans that accrue daily. The scheduled payment stays the same, and how much of it reaches principal depends on when the payment arrives. Paying a week early leaves fewer days of accrued interest and sends more to principal. Paying ten days late does the reverse, and the shortfall is added to what you still owe rather than to a fee.

This is why a payoff quote taken today expires: it is good for a stated number of days, after which the daily accrual has changed it. It is also why an extra payment on a simple interest loan works immediately, with no interest recalculation needed.

Precomputed loans and the rule of 78s

A precomputed loan is different. The whole interest charge is calculated up front and added to the balance, so paying early does not save what you would expect. The rule of 78s allocates that precomputed interest heavily to the early months, leaving a borrower who repays halfway through having paid far more than half the interest.

Federal law limits the practice. Under 15 U.S.C. 1615, a precomputed consumer loan with a term longer than 61 months made after 30 September 1993 has to refund unearned interest by a method at least as favorable to the borrower as the actuarial method, which rules the technique out on longer loans. Shorter loans are not covered, so the rule of 78s still appears on some small installment and auto contracts. If a contract mentions precomputed interest or the rule of 78s, the saving from paying early will be less than this calculator suggests, and that is the point worth checking before signing.