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The Compound Interest EquationP = C (1 + r/n)^{ nt}where P = future value C = initial deposit r = interest rate (expressed as a fraction: eg. 0.06) n = # of times per year interest is compounded t = number of years invested
Simplified Compound Interest EquationWhen interest is only compounded once per year (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 initially 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 repaid. This equation gives the amount B that the person still needs to repay after t years.where B = balance after t years 


