What Is Simple Interest? Formula and Examples

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Simple interest is interest calculated only on the original principal of a loan or deposit. It never accrues on interest that has already built up. If you borrow or invest a fixed sum at a simple interest rate, each period’s interest charge is the same fixed percentage of that original amount. The interest grows in a straight line over time, rather than speeding up the way compound interest does.

What simple interest means

Interest is the price of using someone else’s money. A borrower pays it to a lender, and a bank pays it to a depositor. The rate is quoted as a percentage per period, almost always per year. A 6% annual simple interest rate means $6 of interest per year for every $100 of principal. A 26% annual rate means $26 per year for every $100.

What makes the method “simple” is that the base never changes. With 1% annual simple interest on $100, you receive $1 every year. Under compounding, the second year’s 1% would apply to $101 and pay $1.01, and the third year’s would apply to $102.01 and pay about $1.02. Simple interest ignores that interest-on-interest effect completely. That makes it easy to calculate and easy to predict.

The simple interest formula

The basic equation is:

I = P × r × t

where:

• I = simple interest (in dollars)
• P = principal, the original amount borrowed or deposited
• r = annual interest rate, written as a decimal (6% = 0.06)
• t = time, in years

The rate and the time have to use the same unit. If the rate is annual, time must be in years. Eighteen months is 1.5 years, and 90 days is 90/365 (or 90/360, depending on the convention discussed below).

Total amount: deriving A = P(1 + rt)

Often you want the full amount due or accumulated, not just the interest. The total amount A is the principal plus the interest:

A = P + I A = P + P × r × t A = P(1 + rt)

The last step factors P out of both terms. The expression (1 + rt) works as a growth multiplier. Because t appears as a simple multiplier and not as an exponent, the balance rises by the same dollar amount each period. This linear growth is the defining feature of simple interest.

Solving for rate, time or principal

Because the formula has four variables, you can rearrange it to find any one of them when you know the other three:

• Rate: r = I ÷ (P × t)
• Time: t = I ÷ (P × r)
• Principal: P = I ÷ (r × t)

The “simple interest formula triangle” some textbooks use is just a memory aid for these rearrangements. You put I at the top and P, r and t along the bottom, then cover the variable you want.

Here is a hypothetical example for the rate. You paid $450 of interest on a $5,000 loan over 18 months, so r = 450 ÷ (5,000 × 1.5) = 0.06, or 6% per year.

Here is one for time. At 4% simple interest, $2,000 earns $240 in t = 240 ÷ (2,000 × 0.04) = 3 years.

You cannot calculate the interest from P and r alone. Without a time period the formula gives you a rate of accrual (P × r per year) and not a total.

Converting to a monthly or daily rate

To find the interest for one month, divide the annual rate by 12. A 6% annual rate is 0.5% per month, so $10,000 accrues $50 of interest in a month (10,000 × 0.06 ÷ 12). For a daily rate, divide by the number of days in the year that the lender’s convention uses.

Worked examples

A three-year student loan

Hypothetical example. A student borrows $18,000 at a 6% annual simple interest rate, with the full balance plus interest due in three years.

• Interest: $18,000 × 0.06 × 3 = $3,240
• Total repaid: $18,000 + $3,240 = $21,240

Using the amount formula gives the same result: 18,000 × (1 + 0.06 × 3) = 18,000 × 1.18 = $21,240.

A loan repaid in one lump sum

Hypothetical example. A $10,000 loan at 10% simple interest is due in a single payment after three years, a structure sometimes called a bullet loan. Each year adds $1,000 of interest, so the borrower owes $3,000 in interest and $13,000 in total at maturity.

A savings deposit

Hypothetical example. A $5,000 deposit earning 3% simple interest for four years earns 5,000 × 0.03 × 4 = $600. That is $150 every year, and the balance reaches $5,600.

How simple interest works on real loans

The textbook formula assumes the principal stays put until the end. Most consumer loans are paid down every month, and that changes how much interest you actually pay.

Amortizing loans

On an installment loan such as a car loan, each payment first covers the interest that has accrued since the last payment, and the rest reduces principal. The next period’s interest is then figured on the smaller balance.

Hypothetical example. You owe $10,000 at 6% and pay $300 a month. The first month’s interest is $50 (10,000 × 0.06 ÷ 12), so $250 goes to principal and the balance falls to $9,750. The second month’s interest is $48.75, so $251.25 goes to principal. Interest is never charged on earlier interest, so the method stays simple. The interest portion shrinks each month and the principal portion grows.

The ever-larger principal payments can make an amortizing loan feel as though something is compounding. It is the principal reduction that accelerates, not the interest. The same logic explains why prepaying principal saves money. An extra $1,000 payment removes $1,000 from the balance, so it stops accruing interest for the rest of the term. That also means a larger share of every later payment goes to principal. Biweekly mortgage payment plans work this way. Twenty-six half-payments a year add up to the equivalent of one extra monthly payment, which pays principal down faster and reduces total interest.

If you pay less than the full installment, the payment usually goes to accrued interest first, and only the remainder reduces principal. A short payment can leave the balance almost unchanged.

Daily simple interest

Many auto and personal loans use daily simple interest. Interest accrues each day on the outstanding principal, and the balance is reduced on the day a payment is received rather than on the scheduled due date.

Hypothetical example. On a $10,000 balance at 6%, using a 365-day year, interest accrues at about $1.64 per day (10,000 × 0.06 ÷ 365). Over 30 days that is about $49.32. If you pay five days early, fewer days of interest have built up, so more of the payment reduces principal. If you pay five days late, roughly $8.22 more of the payment goes to interest. Timing matters on these loans in a way it does not when interest is figured monthly on the due date.

Ordinary vs. exact simple interest

When the time period is in days, the result depends on how many days count as a year:

• Exact simple interest uses a 365-day year (366 in a leap year under some conventions).
• Ordinary simple interest uses a 360-day year, a traditional convention in commercial lending.

Hypothetical example. For $10,000 at 6% for 90 days, exact interest is 10,000 × 0.06 × 90/365 ≈ $147.95, and ordinary interest is 10,000 × 0.06 × 90/360 = $150.00. When actual days elapsed are combined with a 360-day year (sometimes called the banker’s rule), the borrower pays slightly more than the stated rate implies over a full year. Your loan agreement states which day-count convention applies.

Where simple interest is used

Simple interest commonly appears in:

• Auto loans, often on a daily simple interest basis.
• Short-term personal loans and installment loans.
• Student loans, where interest typically accrues on the principal balance.
• Mortgages. Standard amortizing home loans in the U.S. charge interest on the outstanding principal each month, though the amortization schedule can make them feel otherwise.
• Bonds. A coupon-paying bond pays a fixed percentage of its face value each period, which is simple interest in action. Coupons that are paid out are not added back to the principal.
• Short-term commercial notes and loans of one period or less, where compounding would make little difference anyway.

Compound interest is more typical of savings accounts and other bank deposits, credit cards, some lines of credit and long-term investments where earnings are reinvested.

Whether a particular loan uses simple interest is set by its contract, not by its category. The disclosure documents state how interest accrues and how payments are applied.

Simple vs. compound interest

Simple interest applies the rate to the original principal only. Compound interest applies it to the principal plus all interest accumulated in earlier periods. The compound interest formula uses the same inputs but raises the growth factor to a power:

Compound interest = P × (1 + r)ⁿ − P

where n is the number of compounding periods (here, years with annual compounding).

Hypothetical comparison. Take a $10,000 loan at 5% for five years:

• Simple interest: 10,000 × 0.05 × 5 = $2,500, so $12,500 total.
• Compounded annually: 10,000 × (1.05)⁵ − 10,000 = $2,762.82, so $12,762.82 total.

The same $10,000 at 10% for three years costs $3,000 under simple interest. Compounded annually, it costs $3,310. The gap is $310 after three years and keeps widening, because compound interest grows exponentially while simple interest grows linearly.

At the same nominal rate, the two methods match over a single compounding period, and compound interest pulls ahead after that. More frequent compounding (quarterly, monthly, daily) widens the difference further. For a borrower, simple interest is the cheaper method. For a saver or investor, compounding is what builds wealth over long horizons. The compound interest guide covers its formula and compounding frequency in detail.

Limitations of simple interest

• It understates growth for savers. If interest is reinvested, simple interest no longer describes what actually happens, and the simple formula will understate the ending balance.
• It is not the full cost of a loan. The formula covers interest only. Origination fees, late fees and other charges are separate, so two loans with the same simple interest rate can cost different amounts. A loan’s APR disclosure includes certain fees that the bare rate does not.
• Results depend on conventions. The day-count basis (360 vs. 365), the payment application order and whether interest accrues daily or monthly all change the dollar figure.
• The basic formula assumes a constant principal. On a loan you pay down every month, I = P × r × t applied to the original amount overstates the interest you will actually pay. Each period must be calculated on the current balance.
• It ignores inflation. A deposit earning a fixed simple rate can lose purchasing power when inflation runs above that rate.

FAQs

The Bottom Line

Simple interest matters most to borrowers with auto, personal, student or mortgage loans, where it costs less than compounding at the same rate. On these loans, paying early or prepaying principal cuts total interest because each period is figured on the current balance. Check the loan contract for the day-count convention, payment order and fees, since the bare rate does not show the full cost.