Simple Interest Calculator

What this simple interest calculator does

Simple interest is the version of interest that behaves itself. It is worked out on the original amount and nothing else. The interest you earned last year does not go on to earn interest of its own, which makes the whole thing a single multiplication instead of a spiral.

So you give this calculator three things: how much money you started with, the annual rate, and how many years. It returns the total interest and the final amount.

There is one thing about it worth knowing before you go further, which is that the phrase "simple interest loan" out in the real world usually does not mean this formula at all. That trips up a lot of people, and it has a section below.

No currency symbol anywhere, deliberately. Put in rupees, dollars, naira, whatever you like. Everything runs in your browser and nothing is stored.

How to use it

1. Principal. The starting amount. The sum you deposited, or the sum you borrowed.
2. Annual Interest Rate. As a percentage, so type 5 rather than 0.05.
3. Years. How long the money sits there.

Two things about what it accepts. It wants a rate of at least 1 percent, and a whole number of years starting at 1. So a 0.5 percent rate or a six month term will be turned away. For anything below those, the arithmetic is short enough to do by hand using the formula below, and we have this on the list to open up.

Press Calculate. Press Reset to clear it.

The formula, and what each letter is doing

Here it is, all of it:

I = P × r × t

Where I is the interest, P is the principal, r is the annual rate as a decimal, and t is the number of years. The final amount is just your principal with the interest stacked on top:

A = P + I

The thing to notice is what is missing. There is no exponent anywhere. In compound interest you raise a growth factor to the power of the number of periods, and that power is what makes compound interest run away from you. Here there is only multiplication, so the money grows in a straight line. Year five earns exactly what year one earned, no more.

Which is why simple interest is generous to a borrower and stingy to a saver. Same formula, opposite feelings.

A worked example you can do on paper

Take 5,000 at 8 percent for 5 years.

The rate as a decimal is 0.08. So the interest is 5,000 × 0.08 × 5 = 2,000.

And the final amount is 5,000 + 2,000 = 7,000.

You can sanity check that a second way, which is often quicker in your head. One year of interest is 5,000 × 0.08 = 400. Five years of that is 400 × 5 = 2,000. Same answer, and it makes the straight line obvious. Every single year adds exactly 400, forever, no matter how long you leave it.

A quick note on what you will see on screen. The tool trims trailing zeros when it prints, so an answer of 2,000.00 shows up as 2000. Same number, just tidier than you might expect.

Careful: a simple interest loan is not this formula

This is the part that costs people real money, so it gets the space it deserves.

Walk into a bank or a dealership and they will happily tell you that your car loan or your personal loan is a "simple interest loan". That is true, and it does not mean I = Prt. What lenders mean by simple interest is that interest is not compounded, so it never gets charged on top of unpaid interest. But it is still charged on your declining balance, recalculated as you pay the loan down.

I = Prt assumes the principal never moves. On a loan you are repaying, it moves every single month.

Here is what the difference looks like on a car.

Nearly double, in the first two. The reason is straightforward once you see it. On the 25,000 car loan you owe the full 25,000 only in month one. By the halfway point you owe roughly half that, so you are being charged interest on roughly half. Averaged across the term you are borrowing a lot less than 25,000, and the interest reflects that.

So if you are pricing a loan that you repay in instalments, this is the wrong tool and it will frighten you unnecessarily. Use an amortisation or loan calculator instead. This one is for money that sits still.

Where I = Prt is exactly right

Plenty of places, and in all of them the principal genuinely does not move.

Fixed deposits that do not compound. Many banks, particularly across South Asia, offer a non cumulative deposit where the interest is paid out to you each period rather than added to the balance. The principal stays put, so this formula is exact.

Treasury bills and discount instruments. You buy below face value and get face value at maturity. No compounding, one payment, straight line. Worth knowing that these usually run on a 360 day year rather than 365, so a sub year calculation needs the day count rather than a year fraction.

Interest only borrowing. Bridging finance, some construction lending, and interest only periods on a mortgage. You service the interest and repay the principal at the end, so the balance never falls during the term.

Promissory notes and informal lending. If you lend a friend money at an agreed rate to be repaid in one lump, this is precisely the arithmetic.

Late payment charges. Statutory interest on overdue invoices is usually simple, accruing on the unpaid amount until it is settled.

Simple against compound, over time

Same 1,000 at 5 percent, one growing in a straight line and the other compounding once a year:

Identical after one year, which surprises nobody, because there is nothing to compound yet. Then the gap opens slowly and then not slowly at all. By year thirty compound has produced 4,322 against simple's 2,500, and the difference is bigger than the original deposit.

There is a neat way to see the same thing through doubling. Under simple interest your money doubles when P × r × t equals P, so t = 1 ÷ r. At 5 percent that is a flat 20 years. Under compound interest at 5 percent it is about 14.2 years, which our rule of 72 calculator will estimate for you in one step.

Across the rates people actually deal with, compound doubles your money roughly 1.4 times faster than simple. Which is a decent thing to carry around in your head next time a product is described to you as paying simple interest.

Questions people ask

What is the formula for simple interest?

I = P × r × t. Principal times the annual rate as a decimal times the number of years. Add that interest to the principal for the final amount.

Can I use this for my car loan?

No, and it will overstate the interest by roughly double. Car loans are repaid in instalments, so the balance falls every month and the interest falls with it. See the section above.

How do I work out simple interest for months?

Turn the months into a fraction of a year and use that as t. Nine months is 0.75. Six months is 0.5. This tool wants whole years of at least one, so do the short ones on paper with the formula.

Is simple or compound interest better?

Depends which side of it you are standing on. Saving, you want compound. Borrowing, you want simple. Over thirty years at 5 percent that preference is worth more than your original principal.

Which currency does it use?

None. It is pure arithmetic with no currency attached, so the answer comes back in whatever you put in.

Can I put in a negative rate?

Not currently. The rate field wants at least 1 percent. Negative and near zero rates exist in the real world, and opening that up is on our list.

References

A note on sourcing. The distinction between simple and compound interest and the arithmetic behind both are standard and set out in the textbooks below. The description of how instalment lending actually accrues interest, which is the point most often confused with this formula, is taken from lenders' own published explanations of their products.

1. OpenStax, Principles of Finance, Section 7.2, Time Value of Money Basics. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics
2. Kellison, S. G., The Theory of Interest, 3rd edition, McGraw-Hill, 2008.
3. Capital One, Simple-Interest Car Loans: What You Need to Know. https://www.capitalone.com/cars/learn/getting-a-good-deal/simpleinterest-car-loans-what-you-need-to-know/2509
4. Bankrate, How to Calculate Loan Interest. https://www.bankrate.com/loans/personal-loans/how-to-calculate-loan-interest/
5. U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Compound Interest Calculator. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator