Simple Interest Calculator

What this simple interest calculator does

Simple interest is the most basic interest formula in finance: a fixed annual rate applied only to the original principal for the entire term. This tool computes the interest you earn (or owe), the total amount at the end, the per-day and per-month interest amounts, and crucially the side-by-side comparison against monthly compound interest. That last comparison is what most people actually need — knowing whether the loan or deposit they're looking at uses simple or compound interest changes the answer by a lot more than people expect over long horizons.

How to Calculate Simple Interest

The formula is famously short. With principal P, annual rate R (as a decimal) and time T (in years):

I = P × R × T

The total amount at the end of the term is:

A = P + I = P × (1 + R × T)

In MathML:

$$I=P\times R\times T$$ $$A=P\times (1+R\times T)$$

When time is given in months, the calculator converts using T = months / 12. When given in days, it uses T = days / 365. These are the two most common day-count conventions in US consumer finance; some institutional products use 360-day years.

Simple versus compound interest

The difference matters whenever (a) the term is long, (b) the rate is high, or (c) the compounding frequency is high. Simple interest grows linearly with time; compound interest grows exponentially. For a one-year term at any normal rate the difference is small. For a 30-year term at 7%, simple interest produces 2.1× the principal but monthly compounding produces about 8.1× — a four-fold difference. The same principle that helps long-term investors hurts long-term borrowers. See the compound interest calculator for the compound side of this comparison.

Numeric example of the divergence

Take $10,000 at 6% for various horizons:

• 1 year — simple: $600 interest; monthly compound: $616.78 interest. Difference: $16.78.
• 5 years — simple: $3,000; monthly compound: $3,488.50. Difference: $488.50.
• 10 years — simple: $6,000; monthly compound: $8,193.97. Difference: $2,193.97.
• 30 years — simple: $18,000; monthly compound: $50,514.99. Difference: $32,514.99.

At one year the difference is negligible; at 30 years the compound figure is nearly three times the simple figure. This is why most savings products advertise APY (compound) and many loan products work hard to legally describe themselves in ways that hide the compounding.

Where simple interest is used

Several real-world products use true simple interest:

• US Treasury bills. T-bills are sold at a discount and computed on a simple-interest basis to maturity.
• Bond accrued interest between coupon dates. Standard convention is simple, day-counted.
• Most US auto loans (simple-interest-on-declining-balance). Each payment first covers accrued simple interest since the last payment, then principal.
• Many personal loans and HELOCs. Especially those that compute interest daily.
• Bridge loans and short-term commercial loans.
• Margin loans at brokerages. Interest accrues daily on the open balance.

Daily simple interest mortgages

A daily simple interest (DSI) mortgage charges interest on the outstanding balance for each calendar day since the last payment, using a daily rate of annual_rate / 365. Compare against a standard mortgage, which assumes payments arrive exactly on the due date and bakes that assumption into the amortization schedule. With DSI, paying ten days early saves ten days of interest; paying ten days late costs ten extra days. Over a 30-year loan the cumulative effect can be material if you regularly send payments early. Use the mortgage calculator for standard amortization or to test how early or late payments affect total interest. Compare borrowing options with the loan calculator.

Add-on interest loans

An add-on loan computes total simple interest upfront (I = P × R × T), adds it to the principal, then divides the sum into equal monthly payments. The catch: even though you're paying down principal over time, the lender charged interest as though the full principal were outstanding all term. The effective APR is roughly twice the stated add-on rate. These structures appear in some installment lending, dealer financing for non-vehicle goods, and historically in older consumer loan products. US truth-in-lending rules require disclosure of the actual APR so it's always shown on the disclosure form.

APR versus APY

Both express an annual rate, but the assumed math is different. APR (Annual Percentage Rate) is a simple-interest-style annual figure — what you pay or receive across a year ignoring intra-year compounding. APY (Annual Percentage Yield) folds in the compounding, so APY ≥ APR whenever the period rate is positive. The conversion is APY = (1 + APR/n)ⁿ - 1, where n is the compounding periods per year. A 5% APR compounded monthly is about 5.116% APY. Loans are quoted in APR by law (truth-in-lending); deposits are typically quoted in APY by law (truth-in-savings). The interest rate calculator handles both directions.

Key Concepts and Definitions

• Principal: the initial dollar amount.
• Rate: the annual percentage, expressed here as a percent (the calculator divides by 100 internally).
• Time: the duration over which interest accrues.
• Day count: the convention used to convert days into years — actual/365 in this tool.
• Simple interest: interest applied only to the original principal.
• Compound interest: interest applied to the running balance including prior interest.
• APR / APY: annual rate quotes that differ by whether intra-year compounding is included.
• Effective rate: the actual rate experienced after the chosen compounding convention.

Comparison: simple vs compound interest

Feature	Simple interest	Compound interest
Formula	I = P × R × T	A = P × (1 + R/n)nT
Growth shape	Linear	Exponential
Effect of compounding frequency	None	Higher frequency → higher A
Common use — deposits	Rare	Standard (APY quoting)
Common use — loans	Auto loans, HELOCs, T-bills	Mortgages (in disclosure), credit cards
Doubling time	1 / R years	~72 / (R×100) years (Rule of 72)
Whose favor it lands in	Borrower over long horizons	Saver over long horizons

Edge Cases and Advanced Scenarios

1. Very long terms. Simple interest understates the cost of borrowing or value of saving by enormous margins past about 10 years. Always force a compound comparison.
2. Partial year accruals. If T is less than 1 (for example 90 days = 0.2466 years), the simple formula handles it directly. Compound formulas need careful handling of fractional periods.
3. Daily versus annual rate confusion. A 0.05% daily rate is not equivalent to a 5% annual rate — daily 0.05% × 365 is 18.25% annualized. Always confirm the period of any quoted rate before using it.
4. Negative rates. Mathematically the formula still works, but negative-rate environments are exotic and usually involve fees rather than literal negative simple interest.
5. Variable principal. The simple formula assumes a fixed principal across the entire term. For amortizing loans the principal drops with each payment; the correct treatment is to apply simple interest to the declining balance each period — exactly what an auto loan does.

The Rule of 72 — for context

The Rule of 72 is a compound-interest mnemonic: divide 72 by the percent rate to estimate doubling time. At 6% it predicts 12 years to double, close to the true 11.9 years at monthly compounding. For simple interest the doubling time is exact: 100 / rate years. At 6% simple that is 16.67 years, almost five extra years for the same money to double. Comparing those two doubling times in your head is the fastest way to internalize why compounding matters.

What To Do With Your Result

• Verify the contract. If a lender quotes a simple-interest figure but the loan compounds monthly behind the scenes, you owe more than the simple calc suggests. Demand the APR disclosure.
• Compare against high-yield savings. The savings calculator projects monthly-compound deposit growth — useful for benchmarking what your principal could earn elsewhere.
• Run the compound counterfactual. The compound figure shown here is exactly that — use it to gauge whether to ask for a different product structure.
• Use it for accrued interest math. Mid-period bond purchases require simple accrued interest; the daily figure here is the right number to multiply by days held.
• Plan partial-year cash flows. Bridge loans, short-term notes and T-bill quotes all use simple interest with day-count conventions; this tool gives a clean, fast answer.

Limitations of this calculator

This tool assumes a flat rate over the entire term, the actual/365 day count for days, and 30-day months when months are selected. It does not amortize a loan (principal stays constant); it does not handle variable-rate products like credit cards; and it does not model fees, taxes, or insurance. For amortizing loans use the loan calculator or mortgage calculator; for compound deposit growth see the compound interest calculator.