Compound Interest Calculator

Calculate the final balance and total interest earned when interest is compounded — annually, semi-annually, quarterly, monthly, or daily. The year-by-year table shows exactly how your balance grows.

Notes

Compound Interest Formula

A = P (1 + \frac{r}{n})^{n t}

Symbol	Meaning	Unit
A	Final amount (principal + interest)	$
P	Principal (initial deposit/investment)	$
r	Annual interest rate as a decimal (r = R/100)	—
n	Number of compounding periods per year	per year
t	Time	years

Compounding Frequency Values

Frequency	n value
Annually	1
Semi-annually	2
Quarterly	4
Monthly	12
Daily	365

Worked Example

P = $5,000, R = 8%, t = 5 years, compounded monthly (n = 12)

A = 5000 (1 + \frac{0.08}{12})^{12 \times 5} = 5000 \times (1.00667)^{60} \approx $7, 449.23

ℹCompound interest earned = $7,449.23 − $5,000 = $2,449.23. Simple interest on the same terms would have been only $2,000.

Effect of Compounding Frequency

More frequent compounding means slightly more interest. For $10,000 at 6% over 10 years:

Compounding	Final Amount	Interest Earned
Annually	$17,908.48	$7,908.48
Semi-annually	$18,061.11	$8,061.11
Quarterly	$18,140.18	$8,140.18
Monthly	$18,193.97	$8,193.97
Daily	$18,220.40	$8,220.40

💡The difference between annual and daily compounding at 6% over 10 years is only $311.92 on a $10,000 investment — frequency matters less than rate and time.

Compound Interest Formula — Full Reference — Variable definitions, derivation, and worked examples
How Compound Interest Works — Detailed Notes — Exponential growth, the Rule of 72, and real-world applications

Frequently Asked Questions

What does compounding frequency mean?

Compounding frequency is how often interest is calculated and added to the principal per year. Monthly compounding (n=12) means interest is computed and added every month, so next month's interest is calculated on a slightly larger balance.

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the stated annual rate before compounding. APY (Annual Percentage Yield) reflects the actual return after compounding. APY = (1 + r/n)^n − 1. For 6% APR compounded monthly: APY = (1 + 0.06/12)^12 − 1 ≈ 6.168%.

How much will $10,000 grow at 7% compounded annually for 20 years?

A = 10,000 × (1 + 0.07)^20 = 10,000 × 3.8697 ≈ $38,697. The investment nearly quadruples without any additional contributions.

What is the Rule of 72?

The Rule of 72 is a shortcut: divide 72 by the annual interest rate to estimate the number of years it takes to double your money. At 8%, money doubles in roughly 72 ÷ 8 = 9 years.