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Simple Interest Formulas The Compound Interest Equation 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 P = C (1 + r/n) nt Simplified Compound Interest Equation P = C (1 + r) t When interest is only compounded once per year (n=1), the equation simplifies to: Continuous Compound Interest When interest is compounded continually (i.e. n --> P=Ce rt ), the compound interest equation takes the form: Demonstration of Various Compounding The 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). (n) Number of Times Compounded (P) Final Principal at the end of one year 1 (yearly) $ 10600.00 2 (semiannually) $ 10609.00 4 (quarterly) $ 10613.64 12 (monthly) $ 10616.78 52 (weekly) $ 10618.00 365 (daily) $ 10618.31 Continuous $ 10618.37 Loan Balance Situation: 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. nt r⎞ ⎛ B = A⎜ 1 + ⎟ ⎝ n⎠ nt r⎞ ⎛ ⎜ 1+ ⎟ − 1 ⎝ n⎠ −P r⎞ ⎛ ⎜ 1+ ⎟ − 1 ⎝ n⎠ Where: B = balance after t years A = amount borrowed n = number of payments per year P = amount paid per payment r = annual percentage rate (APR) Saved C: Math - Simple Interest Formulas http://www.math.com