Introduction to Finance

9

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9.10 Annuity Due Problems
249
key, press the DUE key followed by the FV key to fi nd the future value of an annuity due of 
3506.11, which rounds to $3,506.
Financial Calculator Solution:
Inputs: 3 
8 
–1000
N 
%i 
PMT
Press: DUE FV
Solution: 3506.11
Spreadsheet Solution:
The future value of an annuity due problem is solved by again using Excel’s
 
future value (FV) 
fi nancial function, but adjusting for when the cash fl ows occur, as follows:
= FV(Rate,Nper,Pmt,PV,Type)
= 
FV(.08,3,–1000,0,1)
= 
$3,506.11
Note that the “Type” value was given a “1” to indicate the beginning of period cash fl ows. 
Recall that previously we used a “0” value in “Type” to refl ect cash fl ows occurring at the end 
of each time period.
Present Value of an Annuity Due
Occasionally, you will have to do present value annuity due problems. For example, leasing 
arrangements often require the person leasing equipment to make the fi rst payment at the time 
the equipment is delivered. Let’s illustrate by assuming that lease payments of $1,000 will be 
made at the beginning of each year for three years. If the appropriate interest rate is 8 percent, 
what is the present value of this annuity due leasing problem?
The calculation process to fi nd the present value of this annuity due problem can be 
demonstrated as follows:
PV annuity due = $1,000[1 ÷ (1.08)
0
] + $1,000[1 ÷ (1.08)
1
] + $1,000[1 ÷ (1.08)
2
]
= $1,000(1.000) + $1,000(0.926) + $1,000(0.857)
= 
$1,000(2.783)
= 
$2,783
Notice that by making the fi rst payment now, the present value of this annuity is $2,783. 
This contrasts with a present value of $2,577 if payments are delayed by one year, as would be 
the case with an ordinary annuity.