learn.howToCalculate
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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.
الصيغة
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 (%)
دليل خطوة بخطوة
- 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
أمثلة محلولة
الإدخال
$10,000 at 7% for 20 years, monthly compounding
النتيجة
$40,642 — vs $38,697 with annual compounding
الإدخال
Same with $200/month added
النتيجة
$127,000 — contributions quadruple the outcome
أسئلة شائعة
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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