The Compound Interest Equation P = 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 Equation When interest is only compounded once per year (n=1), the equation simplifies to: P = C (1 + r) t Continuous Compound Interest When interest is compounded continually (i.e. n --> ), the compound interest equation takes the form: P = C e rt 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). As is shown, the method of compounding has little effect. n P 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. B = A (1 + r/n)NT - P (1 + r/n)NT - 1 (1 + r/n) - 1 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)
Posted on: Mon, 08 Jul 2013 05:11:34 +0000
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