Simple Interest Calculator

What simple interest is

Simple interest is interest calculated only on the original principal. If you deposit $1,000 at a 5% annual simple rate, you earn $50 in year one, $50 in year two, and $50 in year three, no matter how much interest has already been paid out. The interest never earns interest of its own. That is the entire idea, and it is what separates simple interest from compound interest, where the balance grows because past interest joins the principal.

Banks, textbooks, and loan agreements use the term in a precise way. A simple interest loan or note accrues interest as a straight line: the same dollar amount each period for the same rate and balance. A simple interest calculation answers a different, narrower question than an amortized loan payment. It tells you the total finance charge on a fixed principal over a fixed time, not what a monthly payment should be.

Simple interest is most accurate for short-term, single-payment arrangements: a personal note between two people, a short bridge loan, a bond that pays a fixed coupon and returns principal at maturity, or a savings estimate where you plan to withdraw the interest each year. It is a planning tool, not a description of how most US consumer loans actually amortize.

This calculator and this page are financial education, not tax, legal, or investment advice. Figures are math estimates based on the inputs you provide and do not account for fees, taxes, penalties, or the terms of any specific agreement.

The simple interest formula, variable by variable

The formula is short enough to memorize: I = P × r × t, where I is the interest, P is the principal, r is the annual interest rate written as a decimal, and t is time in years. The total amount to repay or withdraw is A = P + I, or equivalently A = P × (1 + r × t).

Every variable has one job. P, the principal, is the starting amount borrowed or deposited, in dollars. If you borrow $8,000, P = 8,000. R or r, the annual rate, must match the time unit. When the rate is quoted as a percent, divide by 100 before multiplying: 5% becomes 0.05. If your calculator has a percent field, it does this division for you, which is why the formula here is written as principal × rate ÷ 100 × time.

T or t is time in years. This is the variable people get wrong most often. Nine months is 0.75 years, not 9. Forty-five days at a bank using the 365-day convention is 45/365, or about 0.1233 years. Some lenders and textbooks use a 360-day year for commercial paper, which slightly raises the interest for the same stated rate; if a document specifies a day-count convention, use it.

I is the interest amount, the cost of borrowing or the earnings on deposit. A is the accumulated amount, principal plus interest. Keep the four quantities distinct when you check any figure: interest is the fee, amount is the balance. Mixing them up is the fastest way to double-count.

Units only work if they agree: an annual rate needs time in years. If you have a monthly rate, multiply it by 12 first or convert time to months and adjust the formula. Never multiply an annual rate by a number of months.

Worked examples, step by step

Example 1: a savings deposit. You put $2,500 in an account at 4% simple annual interest for 2 years. Step 1, convert the rate: 4 ÷ 100 = 0.04. Step 2, multiply principal by rate: 2,500 × 0.04 = 100, so the account earns $100 per year. Step 3, multiply by time: 100 × 2 = $200 of interest. Step 4, add the principal: 2,500 + 200 = $2,700 total at the end.

Example 2: a personal loan with days instead of years. You lend a friend $1,200 at 6% for 90 days, counting days on a 365-day year. The rate as a decimal is 0.06. Interest = 1,200 × 0.06 × (90/365) = 1,200 × 0.06 × 0.2466, which is about $17.75. Total to repay is about $1,217.75. The same loan quoted with a 360-day year would accrue 1,200 × 0.06 × (90/360) = $18.00, a 25-cent difference that comes entirely from the day-count convention.

Example 3: solving for the rate. You know the amounts but not the rate. A note repays $5,450 on a $5,000 principal after 18 months. Interest = 450. Rearranged, r = I ÷ (P × t) = 450 ÷ (5,000 × 1.5) = 450 ÷ 7,500 = 0.06, so the note carries a 6% annual simple rate. The same rearrangement solves for time: t = I ÷ (P × r). At $5,000, 6%, and $300 of interest, t = 300 ÷ 300 = 1 year.

Check every example by asking whether the interest is proportional. Double the time should double the interest; double the principal should double the interest; halve the rate should halve it. Simple interest is linear in all three inputs, so any answer that breaks proportionality is wrong.

Simple interest versus compound interest

Compound interest pays interest on interest. After each compounding period, the earned interest is added to the balance, and the next period's interest is computed on the larger amount. Simple interest never does this. The gap between the two starts at zero and grows with both the rate and the time, which is why short-term comparisons look similar and long-horizon comparisons diverge sharply.

The table below shows the same $10,000 at a 5% annual rate under simple interest and under compound interest at three compounding frequencies. Compound figures use A = P × (1 + r/n)^(n×t), where n is the number of compounding periods per year.

Read the table as a rule of thumb: in year one, simple and annually compounded interest are identical, and monthly or daily compounding add only a few dollars. By year ten the annual-compounding gap is about $289, and by year thirty it is about $3,322. Frequency matters less than people expect; duration and rate matter more.

Where simple interest shows up in real life

Personal notes between individuals. Lend a family member $3,000 at 5% for one year and simple interest is the natural way to state the deal: $150 of interest, $3,150 due at maturity. Amortized payment schedules would be overkill for a single repayment.

Bonds and coupons. A standard fixed-coupon bond pays coupon = face value × coupon rate each period and returns the face value at maturity. The coupon never compounds inside the bond, so the interest arithmetic is simple interest on the face amount. (Reinvesting coupons is a separate decision and is where compounding enters.)

Short-term credit. Some auto loans and many subprime installment products are advertised as simple interest loans, meaning interest accrues daily on the outstanding principal and early payments reduce it. The daily accrual is simple interest at t = days/365, but the payment schedule amortizes, so the total finance charge over the loan differs from a single one-shot simple interest figure. Read the contract; the label describes the accrual method, not the payoff math.

Savings estimates with interest withdrawn. If you plan to pocket the interest each year rather than leave it on deposit, your earnings are simple interest by construction, because the balance never grows.

Back-of-envelope comparisons. When you need a fast, conservative answer, such as how much a 9% annual charge costs on a $6,000 balance over 8 months, simple interest gives 6,000 × 0.09 × (8/12) = $360 without needing a spreadsheet.

Common mistakes and how to avoid them

Using months with an annual rate. A $4,000 balance at 12% for 6 months is 4,000 × 0.12 × 0.5 = $240, not 4,000 × 0.12 × 6 = $2,880. Always convert time to years before multiplying.

Comparing a simple interest total to a compound total without matching the terms. Saying compound interest is worse because $16,289 exceeds $15,000 on the same 5% rate over 10 years compares different instruments, not different math. Compounding benefits a saver and costs a borrower; neither number is wrong.

Treating an APR as a simple interest rate. APR on an amortized loan includes fees and reflects a payment schedule. You cannot recover a monthly payment from the simple interest formula, and applying a 7% APR to a full balance for the full term usually overstates the interest an amortized borrower actually pays.

Forgetting the day-count convention. 90 days is 0.2466 years on a 365-day basis and 0.25 on a 360-day basis. On large principals that convention difference is real money.

Rounding intermediate steps. Round only the final dollar-and-cents figure. Rounding the decimal rate or the year fraction first can shift the answer by several dollars.

Assuming the result applies to your loan. This calculator produces a straight-line estimate on a fixed principal. If your agreement amortizes, compounds, capitalizes interest, or charges fees, use a matching tool such as the loan or amortization calculators and treat the simple interest figure as a reference point only.

Limits of this calculator

The calculation assumes a fixed principal, a constant annual rate, and a single lump-sum settlement at the end. It does not model monthly payments, extra principal payments, interest capitalization, changing rates, fees, or taxes on interest income. US federal tax generally applies to interest you earn, and state rules vary; none of that is in the number.

Because the tool is linear, you can scale results mentally: interest per year equals principal × rate ÷ 100, and every additional year adds exactly that amount. If your real situation involves payments over time, the simple interest answer is best read as an upper-bound reference on a full balance, since amortization shrinks the balance that accrues interest.

For amortized loans, compare with the auto loan calculator or the loan comparison calculator. For deposits left to grow, compare with the compound interest calculator, and use the APY calculator when a bank advertises a compounding rate you want to compare against a simple rate. This page is educational and not tax, legal, or investment advice.