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present value interest factor<br />
for an ordinary annuity<br />
The multiplier used to calculate<br />
<strong>the</strong> present value of an ordinary<br />
annuity at a specified discount<br />
rate over a given period of time.<br />
Using Computational Tools to Find<br />
<strong>the</strong> Present Value of an Ordinary Annuity<br />
CHAPTER 4 Time Value of Money 147<br />
TABLE 4.2 The Long Method for Finding<br />
<strong>the</strong> Present Value of an<br />
Ordinary Annuity<br />
Present value<br />
Cash flow PVIF 8%,n a [(1) (2)]<br />
Year (n) (1) (2) (3)<br />
1 $700 0.926 $ 648.20<br />
2 700 0.857 599.90<br />
3 700 0.794 555.80<br />
4 700 0.735 514.50<br />
5 700 0.681<br />
4 7 6 . 7 0 <br />
Present value of annuity $<br />
2 , 7 9 5 . 1 0 a Present value interest factors at 8% are from Table A–2.<br />
Annuity calculations can be simplified by using an interest table for <strong>the</strong> present<br />
value of an annuity, a financial calculator, or a computer and spreadsheet.<br />
The values for <strong>the</strong> present value of a $1 ordinary annuity are given in Appendix<br />
Table A–4. The factors in <strong>the</strong> table are derived by summing <strong>the</strong> present value<br />
interest factors (in Table A–2) for <strong>the</strong> appropriate number of years at <strong>the</strong><br />
given discount rate. The formula for <strong>the</strong> present value interest factor for an ordinary<br />
annuity with cash flows that are discounted at i percent for n periods,<br />
PVIFA i,n, is 9<br />
PVIFA i,n n<br />
t1<br />
1<br />
<br />
(1 i) t<br />
(4.15)<br />
This factor is <strong>the</strong> multiplier used to calculate <strong>the</strong> present value of an ordinary<br />
annuity at a specified discount rate over a given period of time.<br />
By letting PVA n equal <strong>the</strong> present value of an n-year ordinary annuity, letting<br />
PMT equal <strong>the</strong> amount to be received annually at <strong>the</strong> end of each year, and letting<br />
PVIFA i,n represent <strong>the</strong> appropriate present value interest factor for a onedollar<br />
ordinary annuity discounted at i percent for n years, we can express <strong>the</strong><br />
relationship among <strong>the</strong>se variables as<br />
PVA nPMT (PVIFA i,n) (4.16)<br />
9. A ma<strong>the</strong>matical expression that can be applied to calculate <strong>the</strong> present value interest factor for an ordinary annuity<br />
more efficiently is<br />
PVIFAi,n 1 1<br />
1<br />
(4.15a)<br />
i (1i) n<br />
The use of this expression is especially attractive in <strong>the</strong> absence of <strong>the</strong> appropriate financial tables and of any financial<br />
calculator or personal computer and spreadsheet.
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