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Compound interest earns returns on both principal and previously earned interest. The frequency of compounding (annual, monthly, daily) affects the effective annual rate (EAR), with more frequent compounding yielding slightly higher returns.
공식
A = P(1+r/n)^(nt) + PMT×[(1+r/n)^(nt)−1]/(r/n) where PMT=regular payment
- A
- Final Amount ($)
- P
- Principal ($)
- r
- Annual Rate (%)
단계별 가이드
- 1A = P × (1 + r/n)^(n×t)
- 2P = principal, r = annual rate, n = compounding periods/year, t = years
- 3With monthly contributions (PMT): add PMT × ((1+r/n)^(n×t) − 1) ÷ (r/n)
- 4EAR = (1 + r/n)^n − 1
풀어진 예시
입력
$10,000 at 7% for 20 years, monthly compounding
결과
$40,642 — vs $38,697 with annual compounding
입력
Same with $200/month added
결과
$127,000 — contributions quadruple the outcome
자주 묻는 질문
How is compound interest different from simple interest?
Simple interest: I = PRT (linear growth). Compound interest: A = P(1+r)^t (exponential growth). Compound interest accelerates as interest earns interest.
How often should interest compound?
More frequent compounding = higher returns. Annual vs daily compounding can differ by 0.5–1% annually. Continuous compounding (e) is the theoretical maximum.
What is the "Rule of 72"?
Years to double ≈ 72 / interest rate. At 8%, money doubles in ≈9 years. Quick mental estimation for long-term growth.
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