Simple Interest Calculator

What simple interest means

Simple interest is a charge on the money you borrowed, calculated only on the original amount. It does not grow the way a credit card balance grows, because the interest that builds up is never added to the balance and never earns interest of its own.

The formula has three parts and no exponents:

Interest = principal x rate x time, written as I = P x r x t. Principal is the amount borrowed, rate is the yearly rate written as a decimal, and time is the number of years. Borrow $5,000 at 6 percent for 3 years and the interest is 5,000 x 0.06 x 3 = 900 dollars.

That flat structure is why simple interest is easy to check in your head and easy to compare across offers. It is also why it is used on most installment loans, where the balance falls every month and the interest is charged on what is still owed. The Consumer Financial Protection Bureau explains interest the same way: a percentage of the amount you owe, charged for the privilege of borrowing it.

One thing the formula does not capture: on a real installment loan the balance drops with every payment, so the total interest is less than P x r x t applied to the full amount for the full term. The formula gives the exact answer for a lump sum repaid at the end, and a close upper bound for a loan paid down monthly.

The formula in three steps

Take a $5,000 loan at 6 percent for 3 years and run it in order.

1. Turn the rate into a decimal: 6 percent becomes 0.06.
2. Multiply principal by rate: 5,000 x 0.06 = 300. That is the interest for one year.
3. Multiply by the number of years: 300 x 3 = 900.

The total repaid is 5,000 + 900 = 5,900 dollars, and the interest is 18 percent of the amount borrowed.

Run the same numbers with a shorter term and the interest scales down in a straight line. Two years gives 5,000 x 0.06 x 2 = 600. One year gives 300. Six months gives 5,000 x 0.06 x 0.5 = 150. There is no compounding step and no curve, which is what makes this the easy case.

The monthly cost of that interest is the annual charge divided by 12: 300 / 12 = 25 dollars a month. On a loan repaid in equal monthly installments, that $25 figure is the interest portion of the first payment, and it shrinks as the balance falls.

Months and days: setting the term correctly

The formula wants time in years, so any other unit has to be converted first. Months divide by 12 and days divide by 365.

An 18 month loan at 12 percent on $800: the term is 18 / 12 = 1.5 years, so the interest is 800 x 0.12 x 1.5 = 144 dollars.

A 90 day note at 5 percent on $2,000: the term is 90 / 365 = 0.2466 years, so the interest is 2,000 x 0.05 x 0.2466 = 24.66 dollars. Rounding the term to a quarter of a year gives $25, a difference of 34 cents, which matters only if you are checking a lender's figure to the cent.

The day count is where small disagreements come from. Most consumer loans use 365 days, which is what the calculator above does. Some commercial notes and a few older contracts use a 360 day year, which inflates the daily charge by about 1.4 percent. On the $2,000 note, 360 days gives 25.00 instead of 24.66. If a lender quotes a per diem, ask which year length it assumes.

Interest on a loan paid off early is usually charged per day on the remaining balance, so the daily figure is the one to watch: 5,000 x 0.06 / 365 = 0.82 dollars a day on a $5,000 balance at 6 percent.

Simple against compound: the gap in dollars

Compound interest adds the interest to the balance, so the next period charges interest on a larger number. Over one year the two are close. Over ten they are not.

On $10,000 at 6 percent, the first year of compounding costs $17 more than simple interest. By year 10 the gap is $2,194, and by year 20 it is $11,102, more than the original principal. That curve is the whole argument for starting to save early, and the whole reason a credit card balance is harder to clear than it looks.

The compound column uses monthly compounding: 10,000 x (1 + 0.06 / 12) to the power of 120, minus the principal. Daily compounding, which is what most credit cards use, lands a little higher again.

For a borrower choosing between two loans, the gap tells you what a longer term costs in total. A simple interest loan at 6 percent over 5 years charges $3,000 on $10,000. Stretch it to 10 years and the charge doubles to $6,000, even though the rate never moved.

Where you meet simple interest

Simple interest shows up wherever the balance falls as you pay, and wherever a loan is short enough that compounding would be noise.

• Auto loans. Interest accrues daily on the unpaid balance. Pay early and you cut the interest, which is why the payoff quote changes every day.
• Personal and installment loans. Most are simple interest with a fixed payment, and extra payments go straight to principal.
• Short term notes and private loans. A loan between two people or a 90 day business note is almost always written as P x r x t.
• Late payment charges. Many invoices charge a monthly rate on the unpaid amount, which is simple interest by another name.

The other side of the line is just as clear. Savings accounts, CDs, credit cards and mortgages all compound, and a mortgage compounds monthly on a balance that amortizes. If you are comparing a savings product, a simple interest figure understates what you will earn, because the interest you earn starts earning too.

One practical test: read the disclosure for the word "compounded". If it is there, the simple formula will be low by a small amount in year one and a large amount in year ten.

To compare two offers, put each one in the calculator with the same principal and term, then look at the total rather than the rate. A 5 percent loan with a $300 fee over 3 years and a 6 percent loan with no fee are closer than they look: the first costs 10,000 x 0.05 x 3 = 1,500 in interest plus 300 in fees, and the second costs 10,000 x 0.06 x 3 = 1,800. The cheaper rate wins by nothing once the fee is counted, which is the whole point of comparing APR.

For a savings decision the same total tells you what a lump sum will be worth. $10,000 at 5 percent simple interest is worth $11,500 after 3 years. A 5 percent account with monthly compounding reaches $11,614.72, which is $114.72 more for doing nothing beyond leaving the money alone.

APR, add on interest and the fine print

Two loans can both say 6 percent and cost sharply different amounts, because the rate is not the same thing as the annual percentage rate.

APR includes fees and reflects the true yearly cost of credit. A $10,000 loan at 6 percent with a $400 origination fee has an APR above 6 percent, because you received $9,600 and are paying interest on $10,000.

Add on interest is the other trap. A dealer quotes 6 percent "add on" over 4 years, which means the interest is calculated on the full principal for the whole term and then spread across 48 payments. The interest is 10,000 x 0.06 x 4 = 2,400, the payment is 12,400 / 48 = 258.33, and the true APR on that declining balance works out to about 2 x 48 x 6 / 49 = 11.8 percent. The quoted 6 percent is roughly half the real cost.

Any time a lender multiplies the rate by the original balance instead of the remaining balance, run the APR before you sign. The SEC investor glossary entry on simple interest is a short plain language reference for the difference between the two methods.

For a savings goal the same logic runs in reverse. A 5 percent simple interest account pays $500 a year on $10,000, every year, no matter how long you leave it. A 5 percent account that compounds monthly pays $511.62 in year one and more every year after.