What is the difference between compound interest and simple interest?

Simple interest pays only on the original principal. Compound interest pays on principal plus prior interest. Over 20 years at 5%, $10,000 grows to $20,000 with simple interest and about $27,126 with monthly compounding.

How much will 10000 grow in 10 years with compound interest?

At 5% APR compounded monthly with no deposits, $10,000 grows to about $16,470 in 10 years. At 7% monthly it grows to about $20,097. Adding regular monthly deposits increases the ending balance much faster than rate alone.

Compound Interest Calculator

APY · All frequencies · Deposits · Continuous · Full schedule

Principal ?

Annual Rate (APR) ?

Compounding ?

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Optional deposits

Monthly Deposit

Deposit Timing ?

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Tax Rate ?

Inflation ?

📈 Enter principal, rate, and time to see ending balance, APY, schedule, and compound vs simple comparison.

Ending Balance

Total Interest

Effective APY

Principal

Deposits

Interest

After Tax

Inflation Adjusted

Rule of 72

years to double

Formula used

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

total

📈 Growth Over Time

📋 Growth Schedule

Mo	Date	Deposit	Interest	Balance

Compound Interest Formula

Compound interest adds earned interest back to principal so later periods earn interest on interest. The standard formula is:

A = P(1 + r/n)^(nt) A = ending amount · P = principal · r = annual rate · n = compounds per year · t = years

Worked example

$10,000 at 5% APR compounded monthly for 10 years:

A = 10000 × (1 + 0.05/12)^(12×10) = 10000 × (1.0041667)^120 ≈ $16,470.09

Interest earned is $6,470.09. Effective APY = (1 + 0.05/12)^12 − 1 = 5.116%.

With monthly deposits

When you add a fixed deposit C each month, add the future value of an annuity:

FV = C × [((1 + r/n)^(nt) − 1) / (r/n)] Then total = principal growth + deposit growth

Continuous compounding

Continuous compounding is the limit as n goes to infinity:

A = P × e^(rt) e ≈ 2.71828 · same $10,000 at 5% for 10 years ≈ $16,487.21

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Daily and continuous results are nearly identical. The rate and time dominate. Frequency matters most when comparing annual vs monthly.

APY, Rule of 72 & FAQ

Compounding frequency comparison

Frequency	n	APY at 5% APR	$10k after 10 yrs
Annually	1	5.000%	$16,288.95
Quarterly	4	5.095%	$16,436.19
Monthly	12	5.116%	$16,470.09
Daily	365	5.127%	$16,486.65
Continuous	∞	5.127%	$16,487.21

Rule of 72

Years to double ≈ 72 ÷ rate. At 6%, about 12 years. At 8%, about 9 years. Useful for quick mental math, less accurate below 6% or above 10%.

How do you calculate compound interest?

Use A = P(1 + r/n)^(nt). Multiply principal by one plus the rate per period, raised to the number of periods. For continuous compounding use A = Pe^(rt). This calculator also layers monthly deposits onto that growth.

What is the difference between APR and APY?

APR is the stated annual rate. APY includes compounding: APY = (1 + APR/n)^n − 1. Banks advertise APY on savings so you can compare accounts with different compounding schedules.

Does daily compounding earn much more than monthly?

On a 5% APR, monthly APY is about 5.116% and daily about 5.127%. Over 10 years on $10,000 the gap is roughly $17. Raising the rate by 0.1% usually matters more than switching from monthly to daily.

What is the Rule of 72?

Divide 72 by your interest rate to estimate doubling time. At 6%, 72 ÷ 6 = 12 years. At 9%, about 8 years. It is an approximation. Exact doubling time is ln(2) / ln(1 + r).

How does continuous compounding work?

Continuous compounding uses A = Pe^(rt), the upper bound for a given rate and time. It is common in theory and some money market models. For consumer savings accounts, daily compounding is the practical maximum.

Compound Interest vs Simple Interest

Simple interest pays only on the original principal. Compound interest pays on principal plus prior interest. The gap widens every year.

Example: $10,000 at 5% for 20 years. Simple interest ends at $20,000 ($10,000 interest). Monthly compound interest ends near $27,126. The extra $7,126 is interest earned on interest.

Years	Simple @ 5%	Compound monthly @ 5%	Extra from compounding
5	$12,500	$12,833	$333
10	$15,000	$16,470	$1,470
20	$20,000	$27,126	$7,126
30	$25,000	$44,677	$19,677

How much does $10,000 grow with compound interest?

Enter $10,000 principal, your rate, and years above. At 5% monthly for 10 years with no deposits you get about $16,470. Add $200 each month and the balance jumps past $48,000 because deposits also compound.

At 7% monthly for 20 years, $10,000 alone becomes about $40,000. The same principal with $300 monthly deposits can exceed $160,000. Time and consistent deposits matter more than tiny APY differences.

How to calculate compound interest manually

For annual compounding: multiply principal by (1 + rate) once per year. Year 1: $10,000 × 1.05 = $10,500. Year 2: $10,500 × 1.05 = $11,025. Repeat for each year.

For monthly compounding: use monthly rate = APR ÷ 12, then raise (1 + monthly rate) to months. Or use this calculator and export the schedule to verify each step.

Savings accounts, CDs, and taxable interest

High yield savings accounts usually compound daily and pay monthly. Certificates of deposit often compound daily or monthly and pay at maturity or on a set schedule. Always compare APY, not APR, when choosing an account.

Interest from taxable savings is ordinary income in the US. In the 22% bracket you keep 78 cents of each interest dollar. Enter your tax rate above to see after tax balance. Tax deferred or tax free accounts change the after tax result.

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This calculator is for education and planning. Actual bank balances depend on day count methods, rounding, fees, and rate changes. Confirm figures with your bank or advisor before making money decisions.