(In the case of a debt, cash flows are payments against principal and interest; in the case of a financial asset, these are contributions to or withdrawals from the balance.) More generally, the cash flows may not be periodic but may be specified individually.Any of these variables may be the independent variable (the sought-for answer) in a given problem.This principle allows for the valuation of a likely stream of income in the future, in such a way that annual incomes are discounted and then added together, thus providing a lump-sum "present value" of the entire income stream; all of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money.For example, the future value sum There are several basic equations that represent the equalities listed above.

For an annuity that makes one payment per year, i will be the annual interest rate.A typical coupon bond is composed of two types of payments: a stream of coupon payments similar to an annuity, and a lump-sum return of capital at the end of the bond's maturityâ€”that is, a future payment.The two formulas can be combined to determine the present value of the bond.The solutions may be found using (in most cases) the formulas, a financial calculator or a spreadsheet.The formulas are programmed into most financial calculators and several spreadsheet functions (such as PV, FV, RATE, NPER, and PMT).See compound interest for details on converting between different periodic interest rates.

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