Compound interest formula: A = P(1 + r/n)^(nt)
Interest
Compound interest formula: A = P(1 + r/n)^(nt)
Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time the money is invested for in years.
Example
If you invest $1,000 at an annual interest rate of 5% compounded monthly for 10 years, the amount accumulated is A = 1000(1 + 0.05/12)^(12*10) = $1,647.01.
Understanding the compound interest formula helps investors and savers calculate the future value of their investments or savings, enabling them to make informed financial decisions.
Related concepts
d₁ and d₂ are in Black-Scholes: d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T
the Black-Scholes formula prices
Black-Scholes formula: C = S*N(d1) - X*e^(-rT)*N(d2), P = X*e^(-rT)*N(-d2) - S*N(-d1)
Dividend discount model
D₁/(r - g) = stock price
Yield curve
Yield curves show interest rates across different maturities
Rule of 72
Rule of 72 estimates doubling time by dividing 72 by interest rate
Write the Black-Scholes formula for a European call option: C = S·N(d₁) - K·e^(-rT)·N(d₂)
C = S·N(d₁) - K·e^(-rT)·N(d₂)
Educational content, not financial advice.
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