162 PART 2 Important Financial Concepts
annuity
A stream of equal periodic cash
flows, over a specified time
period. These cash flows can be
inflowsof returns earned on
investments or outflowsof funds
invested to earn future returns.
LG3present value, and (2) the longer the period of time, the lower the present value.
Also note that given a discount rate of 0 percent, the present value always equals
the future value ($1.00). But for any discount rate greater than zero, the present
value is less than the future value of $1.00.Comparing Present Value and Future Value
We will close this section with some important observations about present val-
ues. One is that the expression for the present value interest factor foripercent
andnperiods, 1/(1i)n, is theinverseof the future value interest factor fori
percent andnperiods, (1i)n. You can confirm this very simply: Divide a pres-
ent value interest factor foripercent andnperiods,PVIFi,n, given in Table A–2,
into 1.0, and compare the resulting value to the future value interest factor given
in Table A–1 foripercent andnperiods,FVIFi,n,.The two values should be
equivalent.
Second, because of the relationship between present value interest factors
and future value interest factors, we can find the present value interest factors
given a table of future value interest factors, and vice versa. For example, the
future value interest factor (from Table A–1) for 10 percent and 5 periods is
1.611. Dividing this value into 1.0 yields 0.621, which is the present value inter-
est factor (given in Table A–2) for 10 percent and 5 periods.Review Questions
4–3 How is the compounding processrelated to the payment of interest on
savings? What is the general equation for future value?
4–4 What effect would a decreasein the interest rate have on the future value
of a deposit? What effect would an increasein the holding period have on
future value?
4–5 What is meant by “the present value of a future amount”? What is the
general equation for present value?
4–6 What effect does increasingthe required return have on the present value
of a future amount? Why?
4–7 How are present value and future value calculations related?4.3 Annuities
How much will you have at the end of 5 years if your employer withholds and
invests $1,000 of your year-end bonus at the end ofeachof the next 5 years, guar-
anteeing you a 9 percent annual rate of return? How much would you pay today,
given that you can earn 7 percent on low-risk investments, to receive a guaranteed
$3,000 at the end ofeachof the next 20 years? To answer these questions, you
need to understand the application of the time value of money toannuities.
An annuityis a stream of equal periodic cash flows, over a specified time
period. These cash flows are usually annual but can occur at other intervals, such
as monthly (rent, car payments). The cash flows in an annuity can be inflows(the