Managerial decisions often require determining the present value of a stream of future cash flows. Also, we often need to know the amount to which an initial quantity will grow during a specified time period, and at other times we must calculate the interest rate built into a financial contract. The basic concepts involved in these processes are called compounding and the time value of money.

The key procedures covered in this appendix are summarized here:

• Future Value: FVn = PV(1 + i)n, where FVn is the future value of an initial amount, PV, compounded at the rate of i percent for n periods. The term (1 + i)n is the future value interest factor, FVIFin. Values for FVIF are contained in tables.

• Present Value: PV = FVn[1/(1 + i)]n. This equation is simply a transformation of the future value equation. The term [1/(1 + i)]n is the present value interest factor, PVIFin.

• Future Value of an Annuity: An annuity is defined as a series of constant or equal payments of R dollars per period. The sum, or future value of an annuity, is given the symbol Sn, and it is found as follows: Sn = R

The term

t=i is the future value interest factor for an annuity, FVIFA,n.

Present Value of an Annuity: The present value of an annuity is identified by the symbol

. The term

= PVIFAin is the present value interest factor for an annuity.

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