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The Compound Interest Equation
P = C (1 + r/n) ntwhere
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = # of times per year interest in compounded
t = number of years invested
Simplified Compound Interest EquationWhen interest is only compounded once per yer (n=1), the equation simplifies to:
P = C (1 + r) t
Continuous Compound InterestWhen interest is compounded continually (i.e. n --> ), the compound interest equation takes the form:
P = C e rt
Demonstration of Various CompoundingThe following table shows the final principal (P), after t = 1 year, of an account initally with C = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.
Loan BalanceSituation: A person initially borrows an amount A and in return agrees to make n repayments per year, each of an amount P. While the person is repaying the loan, interest is accumulating at an annual percentage rate of r, and this interest is compounded n times a year (along with each payment). Therefore, the person must continue paying these installments of amount P until the original amount and any accumulated interest is repayed. This equation gives the amount B that the person still needs to repay after t years.
B = balance after t years