Як розрахувати Compound Interest
Що таке Compound Interest?
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.
Формула
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 (%)
Покрокова інструкція
- 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
Розв'язані приклади
Введення
$10,000 at 7% for 20 years, monthly compounding
Результат
$40,642 — vs $38,697 with annual compounding
Введення
Same with $200/month added
Результат
$127,000 — contributions quadruple the outcome
Часті запитання
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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