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Compound Interest Formula
Financial Math • Grades 8, 9, 10, 11
Financial Math
Compound Interest Formula
Calculate exponential compound interest growth with A = P(1 + r/n)ⁿᵗ.
The Formula
A = P(1 + r/n)ⁿᵗ
Used for: Calculating exponential growth on deposits or loans compounded annually, monthly, or daily
AFinal accumulated amount balance
PInitial principal balance
rAnnual nominal interest rate (decimal)
nCompounding frequency per year (e.g. 12 = monthly)
tTime in years
⚡Live Interactive Quick Solver
Instant CalculationCompound Balance (A):$1,161.47
Total Compound Interest: $161.47• Step: A = 1000(1 + 0.05/12)^(12×3)
A = P\left(1 + \frac{r}{n}\right)^{nt}
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
💰
A = P(1 + r/n)ⁿᵗInterest earns interest over time, compounding exponentially.
🔄
Compounding Frequency (n)n = 1 (Annual), n = 4 (Quarterly), n = 12 (Monthly), n = 365 (Daily).
📝 Worked Examples & Step-by-Step Solutions
Example 1: $1,000 at 6% Compounded Monthly for 5 Years
Problem:
P = 1000, r = 0.06, n = 12, t = 5 years.1
Rate per period
r/n = 0.06 / 12 = 0.0052
Total periods
n × t = 12 × 5 = 603
Calculate
A = 1000 × (1 + 0.005)⁶⁰ = 1000 × 1.34885 ≈ $1,348.85Answer: A ≈ $1,348.85 (Interest: $348.85)
💡 Pro Tips & Common Mistakes
Rule of 72
Approximate years to double your money = 72 / (Interest Rate %).
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