Question 1

What is compound interest?

Accepted Answer

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, it grows exponentially. Albert Einstein reportedly called it "the eighth wonder of the world."

Question 2

What is the compound interest formula?

Accepted Answer

A = P(1 + r/n)^(nt), where A = final amount, P = principal, r = annual interest rate (decimal), n = compounding periods per year, t = time in years. For continuous compounding: A = Pe^(rt).

Question 3

What is the difference between APR and APY?

Accepted Answer

APR (Annual Percentage Rate) is the nominal rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding — it is always higher than APR for the same loan or investment. Our calculator shows the Effective Annual Rate (EAR = APY).

Question 4

How does compounding frequency affect returns?

Accepted Answer

More frequent compounding produces higher returns. For 10% nominal rate: annual compounding yields 10%, monthly yields ~10.47%, daily ~10.52%, and continuous ~10.52%. The difference narrows as frequency increases.

Question 5

What is continuous compounding?

Accepted Answer

Continuous compounding is the mathematical limit where interest is compounded infinitely often. The formula is A = Pe^(rt). It produces the maximum possible return for a given nominal rate and is used in options pricing and theoretical finance.

Question 6

How are regular contributions calculated?

Accepted Answer

Regular contributions use the future value of an ordinary annuity: FV = C × [(1+r/n)^(nt) − 1] / (r/n). This is added to the principal's compound growth. Total final value = principal growth + contribution growth.

Frequency	Periods/Year (n)	EAR at 10% nominal
Annually	1	10.0000%
Semi-Annual	2	10.2500%
Quarterly	4	10.3813%
Monthly	12	10.4713%
Weekly	52	10.5065%
Daily	365	10.5156%
Continuous	∞	10.5171%

Compound Interest Calculator

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Frequently Asked Questions

What is compound interest?

What is the compound interest formula?

What is the difference between APR and APY?

How does compounding frequency affect returns?

What is continuous compounding?

How are regular contributions calculated?

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