Calculate future value with periodic or continuous compounding using exponential growth formulas.
A = P(1 + r/n)^(nt)
| Variable | Meaning |
|---|---|
| P | Principal — initial amount invested or borrowed |
| r | Annual interest rate as a decimal (e.g. 5% → 0.05) |
| n | Number of times interest compounds per year |
| t | Time in years |
| A | Final amount (principal + interest) |
Common n values:
Annually = 1 · Semi-annually = 2 · Quarterly = 4 · Monthly = 12 · Daily = 365
The effective APY (annual percentage yield) accounts for compounding and is always slightly higher than the nominal rate r:
APY = (1 + r/n)^n − 1
A = Peʳᵗ (continuous)
As n → ∞, the periodic formula (1 + r/n)^(nt) approaches the natural exponential e^(rt). This is the mathematical limit of compounding more and more frequently.
Continuous compounding always gives a slightly higher return than any finite n, but the difference shrinks as n grows larger.
For 5% annually over 5 years with $1,000:
Monthly (n=12): $1,283.36
Daily (n=365): $1,284.00
Continuous: $1,284.03
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