finance calculator

Interest Calculator

Calculate simple and compound interest scenarios instantly to see how principal, rate, and time affect your total earnings.

Formula Verified by Dr. Elizabeth Vance, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Principal$

Annual rate%

Years

Compounds per year

Results

Compound total

$12,834

Compound interest$2,834

Simple interest$2,500

Simple total$12,500

Effective annual rate5.12%

Tip

Return when comparing rates, compounding frequencies, and different time periods across loans or savings products.

Formula

Compound interest formula

A = P(1 + r/n)^(nt)

Compound interest applies interest to both the original principal and accumulated interest each compounding period.

Step by step

How the calculation works

1Enter principal, annual rate, time, and compounding frequency.
2The calculator compares simple interest with compound interest.
3The effective annual rate shows the real annualized effect of compounding.

Example

Interest example

A $10,000 balance at 5% compounded monthly for 5 years grows to about $12,834.

Related guides

Learn more about this calculation

Guide

Compound Interest: Formula, Examples, and Calculator

Learn how compound interest works, calculate growth with monthly deposits, compare assumptions, and avoid common projection mistakes.

Guide

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Compare simple interest and monthly compound interest, learn when each model fits, and use worked examples aligned to the calculators.

Simple vs compound results

Compare simple interest, compound interest, and final totals.

How to understand and use this calculator

What This Calculator Does

This calculator runs the same principal, rate, and time period through both the simple interest formula and the compound interest formula at once, so you can see the dollar gap between them directly rather than calculating each separately. It also computes the effective annual rate — the true annualized return once compounding is factored in — which is the number that actually lets you compare two accounts or loans quoted with different compounding frequencies on equal footing.

How to Use This Calculator

Enter the principal, the stated annual interest rate, the number of years, and how many times per year interest compounds (12 for monthly, 4 for quarterly, 365 for daily, 1 for annually).

The calculator returns both the simple-interest total and the compound-interest total for the same inputs, plus the effective annual rate — increase the compounding frequency to see how much faster the compound total grows relative to simple interest.

The Formulas Behind Both Methods

Simple interest:

I_(simple) = P × r × t

Compound interest:

A_(compound) = P (1 + r/n)^(nt)

Effective annual rate (EAR):

EAR = (1 + r/n)^(n) - 1

Where P is principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years.

Worked Example: $10,000 at 5% for 5 Years, Compounded Monthly

Principal of $10,000, a 5% annual rate, a 5-year term, compounded monthly (n = 12).

Simple interest: $10,000 × 0.05 × 5 = $2,500, for a total of $12,500.

Compound interest: $10,000 × (1 + 0.05/12)^(12×5) ≈ $12,833.59 — $2,833.59 in interest, about $333.59 more than the simple-interest method on identical inputs.

Effective annual rate: (1 + 0.05/12)^12 − 1 ≈ 5.12%, slightly above the 5% nominal rate quoted — that extra 0.12 percentage points is purely the effect of monthly compounding.

How Compounding Frequency Changes the Result

On the same $10,000 principal, 5% rate, and 5-year term, moving from annual compounding (n = 1) to monthly (n = 12) to daily (n = 365) increases the total slightly at each step — annual compounding produces the lowest compound total, and daily produces the highest, though the jump from monthly to daily is much smaller than the jump from annual to monthly. This is why two savings accounts advertising the same nominal APR can pay out slightly different amounts: the one compounding more frequently has a marginally higher effective annual rate, even though the quoted rate looks identical.

Why This Matters for Both Savers and Borrowers

For savings, CDs, and investments, more frequent compounding works in your favor — interest starts earning its own interest sooner, so the effective rate you actually earn edges above the stated rate. For loans and credit card balances, the same math works against you: compounding means unpaid interest gets added to the balance and starts accruing interest itself, which is why carrying a credit card balance (often compounding daily) grows so much faster than the card's quoted APR alone would suggest. Understanding which side of the equation you're on — earning compounding or paying it — is the practical reason to run both numbers side by side rather than looking at the stated rate alone.

APR vs. APY: Why Two Rates Get Quoted for the Same Product

APR (Annual Percentage Rate) is the nominal rate before compounding is applied — it's a simple annualized figure that ignores how often interest is actually added to the balance. APY (Annual Percentage Yield), which is the same concept as the effective annual rate this calculator computes, includes the compounding effect and is always equal to or higher than the APR for the same product. Regulations generally require lenders to advertise APR (making loans look cheaper) and require savings institutions to advertise APY (making returns look better) — knowing which figure you're looking at, and converting between them with this calculator, prevents comparing two products on mismatched terms.

The Rule of 72: A Fast Mental Shortcut

Before running exact numbers, the Rule of 72 gives a quick doubling-time estimate: divide 72 by the annual interest rate to get roughly how many years an investment takes to double under compounding. At 6%, that's 72 ÷ 6 = 12 years; at 9%, it's about 8 years. It's an approximation (most accurate in the 6–10% range) rather than an exact formula, but it's a useful sanity check before diving into the precise compound interest calculation above — if the exact math and the Rule of 72 estimate are wildly different, it's worth double-checking the inputs.

Adjusting for Inflation: Nominal vs. Real Return

Every rate this calculator produces is nominal — it doesn't account for inflation eroding the purchasing power of the interest you earn. To find your real return, subtract the inflation rate from the nominal (or effective annual) rate: earning a 5.12% effective annual rate while inflation runs at 3% leaves a real return of roughly 2.12%. That gap matters most for long-term savings and CDs, where a nominally attractive rate can still barely outpace — or even lose to — rising prices, making the effective annual rate this calculator computes only half the picture for real long-term planning.

Related Calculators

For a straightforward simple-interest-only calculation, use the simple interest calculator; for recurring monthly contributions on top of a starting balance, switch to the compound interest calculator.

Related concepts

Simple interest

Interest calculated only on the original principal, growing in a straight line.

Compound interest

Interest calculated on principal and prior accumulated interest, growing exponentially.

Effective annual rate

The real annualized return once compounding frequency is factored in.

APR vs. APY

APR is the nominal stated rate; APY (or EAR) reflects the true rate after compounding.

Rule of 72

A quick mental shortcut for estimating how many years it takes an investment to double at a given rate.

Frequently Asked Questions

What is the difference between simple and compound interest?+

Simple interest only applies to principal. Compound interest applies to principal plus accumulated interest.

What does compounds per year mean?+

It is how many times interest is applied during a year, such as monthly, quarterly, or daily.

Why is effective annual rate higher than the stated rate?+

When interest compounds within the year, the annualized effect can be slightly higher than the nominal rate.

What is the Rule of 72?+

The Rule of 72 is a quick mental formula to estimate how long it will take an investment to double in value. Divide 72 by your annual interest rate (e.g., at 6% interest, your money doubles in approximately 12 years).

How does inflation affect my interest rate return?+

Inflation erodes the purchasing power of money. To find the "real rate of return," you subtract the inflation rate from your nominal interest rate. If you earn 4% interest but inflation is 3%, your real return is only 1%.

What is the difference between APR and APY?+

APR (Annual Percentage Rate) is the nominal annual rate that does not account for the compounding of interest within the year. APY (Annual Percentage Yield) accounts for compounding, reflecting the true interest earned or paid.

How does compounding frequency affect my savings over time?+

More frequent compounding (e.g., daily instead of annually) results in faster interest growth because interest is added to your balance sooner. While the difference is small initially, it compounds into larger sums over long periods.

How is interest calculated on a credit card balance?+

Credit cards calculate interest using a daily periodic rate (APR divided by 365) multiplied by your average daily balance. If you do not pay your statement balance in full monthly, interest compounds daily on all charges.

Are my interest earnings taxable?+

Yes, interest earned on standard bank savings accounts, certificates of deposit (CDs), and bonds is generally taxed as ordinary income in the year it is received, and banks report this to tax authorities using Form 1099-INT.

What is a negative interest rate?+

A negative interest rate is an unconventional monetary policy where commercial banks are charged to deposit cash with the central bank, and retail customers may theoretically pay banks to store their money rather than earning interest.

How does the Federal Reserve interest rate affect my savings?+

The Federal Reserve sets the federal funds rate, which is the interest rate banks charge each other for overnight loans. When the Fed raises this rate, banks typically raise the rates they offer on HYSAs and charge on consumer loans.

What is nominal interest vs. real interest?+

Nominal interest is the stated interest rate on a contract or account without any adjustments. Real interest is the nominal rate adjusted for inflation, representing the actual increase in purchasing power.

Why does daily compounding barely beat monthly compounding?+

The mathematical gain from adding more compounding periods shrinks quickly — going from annual to monthly compounding makes a meaningful difference, but going from monthly to daily adds only a small fraction more, since the formula is approaching its continuous-compounding limit.

Should I use this calculator for a loan or a savings account?+

Both — the same formulas apply either way. For a loan, the compound total represents what you would owe if interest capitalizes; for savings or investments, it represents what your balance would grow to.

How do I find my real, inflation-adjusted return?+

Subtract the inflation rate from the effective annual rate this calculator computes. A 5.12% effective rate with 3% inflation leaves a real return of about 2.12%.

Simple vs compound results

Compare simple interest, compound interest, and final totals.

How to understand and use this calculator

What This Calculator Does

How to Use This Calculator

Enter the principal, the stated annual interest rate, the number of years, and how many times per year interest compounds (12 for monthly, 4 for quarterly, 365 for daily, 1 for annually).

The Formulas Behind Both Methods

Simple interest:

I_(simple) = P × r × t

Compound interest:

A_(compound) = P (1 + r/n)^(nt)

Effective annual rate (EAR):

EAR = (1 + r/n)^(n) - 1

Where P is principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years.

Worked Example: $10,000 at 5% for 5 Years, Compounded Monthly

Principal of $10,000, a 5% annual rate, a 5-year term, compounded monthly (n = 12).

Simple interest: $10,000 × 0.05 × 5 = $2,500, for a total of $12,500.

Compound interest: $10,000 × (1 + 0.05/12)^(12×5) ≈ $12,833.59 — $2,833.59 in interest, about $333.59 more than the simple-interest method on identical inputs.

Effective annual rate: (1 + 0.05/12)^12 − 1 ≈ 5.12%, slightly above the 5% nominal rate quoted — that extra 0.12 percentage points is purely the effect of monthly compounding.

How Compounding Frequency Changes the Result

Why This Matters for Both Savers and Borrowers

APR vs. APY: Why Two Rates Get Quoted for the Same Product

The Rule of 72: A Fast Mental Shortcut

Adjusting for Inflation: Nominal vs. Real Return

Related Calculators

Related concepts

Simple interest

Interest calculated only on the original principal, growing in a straight line.

Compound interest

Interest calculated on principal and prior accumulated interest, growing exponentially.

Effective annual rate

The real annualized return once compounding frequency is factored in.

APR vs. APY

APR is the nominal stated rate; APY (or EAR) reflects the true rate after compounding.

Rule of 72

A quick mental shortcut for estimating how many years it takes an investment to double at a given rate.

Frequently Asked Questions

What is the difference between simple and compound interest?+

Simple interest only applies to principal. Compound interest applies to principal plus accumulated interest.

What does compounds per year mean?+

It is how many times interest is applied during a year, such as monthly, quarterly, or daily.

Why is effective annual rate higher than the stated rate?+

When interest compounds within the year, the annualized effect can be slightly higher than the nominal rate.

What is the Rule of 72?+

How does inflation affect my interest rate return?+

What is the difference between APR and APY?+

How does compounding frequency affect my savings over time?+

How is interest calculated on a credit card balance?+

Are my interest earnings taxable?+

What is a negative interest rate?+

How does the Federal Reserve interest rate affect my savings?+

What is nominal interest vs. real interest?+

Why does daily compounding barely beat monthly compounding?+

Should I use this calculator for a loan or a savings account?+

How do I find my real, inflation-adjusted return?+

Subtract the inflation rate from the effective annual rate this calculator computes. A 5.12% effective rate with 3% inflation leaves a real return of about 2.12%.

Interest Calculator

Inputs

Results

Compound interest formula

How the calculation works

Interest example

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Interest Calculator

Inputs

Results

Key output metrics

Simple vs compound results

Compound balance timeline

How to understand and use this calculator

What This Calculator Does

How to Use This Calculator

The Formulas Behind Both Methods

Worked Example: $10,000 at 5% for 5 Years, Compounded Monthly

How Compounding Frequency Changes the Result

Why This Matters for Both Savers and Borrowers

APR vs. APY: Why Two Rates Get Quoted for the Same Product

The Rule of 72: A Fast Mental Shortcut

Adjusting for Inflation: Nominal vs. Real Return

Related Calculators

Related concepts

Frequently Asked Questions

Compound interest formula

How the calculation works

Interest example

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Key output metrics

Simple vs compound results

Compound balance timeline

How to understand and use this calculator

What This Calculator Does

How to Use This Calculator

The Formulas Behind Both Methods

Worked Example: $10,000 at 5% for 5 Years, Compounded Monthly

How Compounding Frequency Changes the Result

Why This Matters for Both Savers and Borrowers

APR vs. APY: Why Two Rates Get Quoted for the Same Product

The Rule of 72: A Fast Mental Shortcut

Adjusting for Inflation: Nominal vs. Real Return

Related Calculators

Related concepts

Frequently Asked Questions