Math Tables: Interest and Exponential Growth


The Compound Interest Equation

P = C (1 + r/n) nt
    P = future value
    C = initial deposit
    n = # of times per year interest in compounded
    t = number of years invested

Simplified Compound Interest Equation

When interest is only compounded once per yer (n=1), the equation simplifies to:
P = C (1 + r) t

Continuous Compound Interest

P = C e rt

Demonstration of Various Compounding

The following table shows the final principal (P), after t = 1 year and t = 10 years, of an account initally with C = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding (n) has an effect that is initially small but becomes more significant over time (t).
nP (t=1)P (t=10)
1 (yearly)$ 10600.0017908.48
2 (semi-anually)$ 10609.0018061.11
4 (quarterly)$ 10613.6418140.18
12 (monthly)$ 10616.7818193.97
52 (weekly)$ 10618.0018214.89
365 (daily)$ 10618.3118220.27
continuous$ 10618.3718221.19

Loan Balance

B = A (1 + r/n)nt - P (1 + r/n)nt - 1
(1 + r/n) - 1
B = balance after t years
A = amount borrowed
n = number of payments per year
P = amount paid per payment
r = annual percentage rate (APR)