CP

The Present Value Interest Factor of an Annuity for i and n, PVIFAi,n,is a short-

hand notation for the formula.

1. NUMERICAL SOLUTION:

The lower section of the time line shows the numerical solution, $272.32, calculated

by using the first line of Equation 2-5, where the present value of each cash flow is

found and then summed to find the PV of the annuity. If the annuity has many pay-

ments, it is easier to use the third line of Equation 2-5:

2. FINANCIAL CALCULATOR SOLUTION

Inputs: 3 5 
 100 0

Output: 272.32

Enter N 3, I 5, PMT 
100, and FV 0, and then press the PV key to find the

PV, $272.32.

3. SPREADSHEET SOLUTION

$100

°

1 

1

(10.05)^3

0.05

¢

$100(2.7232)$272.32.

PVAnPMT

°

1 

1

(1i)n

i

¢

Present Value of an Annuity 75

ABCDE

1 Interest rate 0.05

2 Time 012 3

3 Cash flow 100 100 100

44 Present value $272.32

In Excel,put the cursor on Cell B4 and then click the function wizard, Financial, PV,

and OK. Then enter B1 or 0.05 for Rate, E2 or 3 for Nper, 
100 for Pmt, 0 or leave

blank for Fv, and 0 or leave blank for Type. Then, when you click OK, you get the an-

swer, $272.32.

One especially important application of the annuity concept relates to loans with

constant payments, such as mortgages and auto loans. With such loans, called amor-

tized loans,the amount borrowed is the present value of an ordinary annuity, and the

payments constitute the annuity stream. We will examine constant payment loans in

more depth in a later section of this chapter.

Time Value of Money 73